Authors:David J. Luitz; Yevgeny Bar Lev Abstract: Recent studies point towards nontriviality of the ergodic phase in systems exhibiting many-body localization (MBL), which shows subexponential relaxation of local observables, subdiffusive transport and sublinear spreading of the entanglement entropy. Here we review the dynamical properties of this phase and the available numerically exact and approximate methods for its study. We discuss in which sense this phase could be considered ergodic and present possible phenomenological explanations of its dynamical properties. We close by analyzing to which extent the proposed explanations were verified by numerical studies and present the open questions in this field.The authors discuss the question of ergodicity and thermalization in disordered, interacting and isolated quantum systems, exhibiting many body localization at strong disorder. For weak disorder, such systems are ergodic and thermalize, however display anomalous static and dynamical properties. In this review the authors survey the literature and the available numerical techniques to study the ergodic phase preceding many body localization and elaborate on the notion of ergodicity in isolated quantum systems. PubDate: 2017-05-15T01:20:57.016343-05: DOI: 10.1002/andp.201600350

Authors:Johannes Wanner; Ulrich Eckern, Karl-Heinz Höck Abstract: Group theoretical methods and k·p theory are combined to determine spin-dependent contributions to the effective conduction band Hamiltonian. To obtain the constants in the effective Hamiltonian, in general all invariants of the Hamiltonian have to be determined. Hence, we present a systematic approach to keep track of all possible invariants and apply it to the k·p Hamiltonian of crystals with zinc-blende symmetry, in order to find all possible contributions to effective quantities such as effective mass, g-factor and Dresselhaus constant. Additional spin-dependent contributions to the effective Hamiltonian arise in the presence of strain. In particular, with regard to the constants C3 and D which describe spin-splitting linear in the components of k and ε, considering all possible terms allowed by symmetry is crucial.An effective – low energy – description of electronic properties is crucial in many areas of solid state physics, in particular, for the development of semiconductor based devices. In this context, the standard model, the so called k·p theory, is re-examined in order to determine the spin-dependent contributions to the effective conduction band Hamiltonian. New contributions are found which describe strain-dependent spin-splitting. PubDate: 2017-05-15T01:20:38.83649-05:0 DOI: 10.1002/andp.201600218

Authors:Ariel Fernandez Abstract: A theory of dielectric response of water under nanoscale confinement was long overdue. This work addresses the problem by establishing a relation between dielectric response and hydrogen-bond frustration subsumed in a non-Debye polarization term. The results hold down to the single-molecule contribution and are validated vis-à-vis experimental measurements on a system where dielectric modulation entails removal of a single water molecule. The frustrated dielectric response down to molecular scales is assessed by contrasting two enantiomeric ligands in association with the same protein, with the complexes differing in the removal of a single interfacial water molecule.Water confined in nanoscale cavities behaves fundamentally differently from bulk solvent, especially in its dielectric response, and a nanoscale theory of water dielectrics was long overdue. This work addresses the challenge by establishing a relation between dielectric response and hydrogen-bond frustration subsumed in spontaneous polarization effects. The results hold down to the single-molecule contribution and are validated vis-à-vis experimental measurements on dielectric modulation involving removal of a single water molecule. PubDate: 2017-05-11T03:26:48.663978-05: DOI: 10.1002/andp.201600373

Authors:John Z. Imbrie; Valentina Ros, Antonello Scardicchio Abstract: We review the current (as of Fall 2016) status of the studies on the emergent integrability in many-body localized models. We start by explaining how the phenomenology of fully many-body localized systems can be recovered if one assumes the existence of a complete set of (quasi)local operators which commute with the Hamiltonian (local integrals of motions, or LIOMs). We describe the evolution of this idea from the initial conjecture, to the perturbative constructions, to the mathematical proof given for a disordered spin chain. We discuss the proposed numerical algorithms for the construction of LIOMs and the status of the debate on the existence and nature of such operators in systems with a many-body mobility edge, and in dimensions larger than one.Many-body localized systems may be considered as a peculiar class of integrable systems, characterized by extensively many conserved operators, whose quasi-local structure is responsible for the suppression of transport and thermalization. We present a review of the theoretical results concerning this emergent integrability in interacting, quantum disordered systems exhibiting localization. PubDate: 2017-05-11T01:56:10.16395-05:0 DOI: 10.1002/andp.201600278

Authors:Muhammad Umar; Kyungtaek Min, Heonsu Jeon, Sunghwan Kim Abstract: Organic distributed feedback (DFB) lasers can be useful photonic tools for biological applications where the roles of organic materials are important, because highly coherent single mode emission with broad tuning range can be obtained. However, the formulaic structures of organic lasers, and the uses of gain media as resonators themselves, are not suitable for inducing laser emission from irregular shaped gain media, such as dye-staining cells and tissues. Here, we report a reusable photonic template comprising an exceedingly thin and discrete titanium dioxide (TiO2) layer on a one-dimensional (1D) quartz grating to induce single mode DFB lasing from a variety of states of optical gain media. Using the same template, the external gain media of optically thick and thin casted film, liquid, and a free-standing thick film reveal single mode lasing with reliable performance. Numerical simulations demonstrate that the 25-nm thick TiO2 disconnected grating lines support a spatially confined DFB mode in the vertical direction, even under no index difference between superstrate and substrate. Additionally, not using the typical waveguide gain layer promises high sensitivity and detection limit in refractometric sensing. These results suggest that the photonic structure may serve as a versatile sensing platform for bioapplications.An exceedingly thin TiO2 (25 nm) is utilized to induce a single mode DFB lasing from arbitrary morphologies of gain media. The grating template supports the TE mode propagating through the TiO2 thin layer. High dependence of the DFB mode on the refractive index of superstrate gain promises a highly sensitive refractometric sensor application. PubDate: 2017-05-11T01:50:38.787479-05: DOI: 10.1002/andp.201700034

Abstract: Interfering optical vortices generate centrifugal traps and shot ramp for neutral atoms. The phenomena rely on the highly non-linear dynamics of the atomic charge in high-intensity laser fields that carries orbital angular momenta. The interference pattern of optical vortices enables controllable sub-optical wavelength traps with a structure tuneable by the optical vortices topological charges.A detuning between the frequencies of the interfering pulses set, the trapped atoms in controlled rotation.(Image: D. Schulze et al.; article number 1600379 in this issue). PubDate: 2017-05-03T01:28:17.32304-05:0 DOI: 10.1002/andp.201770040

Abstract: Flexible control over the directive emissions toward pre-designed directions has attracted long-term interest, but available devices suffer from bulky size, limited functionalities, and low efficiencies. Here, a novel anisotropic meta-atom exhibiting a low polarization cross-talking was proposed, based on which high-efficiency metasurfaces with arbitrary polarization-dependent phase profiles can be easily designed, to realize the desired beam-control functionalities. The strategy paves the way for the realization of high-performance multifunctional optical devices with high integration.(Image: H.-X. Xu et al.; article number 1700045 in this issue) PubDate: 2017-05-03T01:28:16.054487-05: DOI: 10.1002/andp.201770044

Authors:Dong-Ling Deng; Sriram Ganeshan, Xiaopeng Li, Ranjan Modak, Subroto Mukerjee, J. H. Pixley Abstract: We review the physics of many-body localization in models with incommensurate potentials. In particular, we consider one-dimensional quasiperiodic models with single-particle mobility edges. A conventional perspective suggests that delocalized states act as a thermalizing bath for the localized states in the presence of of interactions. However, contrary to this intuition there is evidence that such systems can display non-ergodicity. This is in part due to the fact that the delocalized states do not have any kind of protection due to symmetry or topology and are thus susceptible to localization. A study of such incommensurate models, in the non-interacting limit, shows that they admit extended, partially extended, and fully localized many-body states. Non-interacting incommensurate models cannot thermalize dynamically and remain localized upon the introduction of interactions. In particular, for a certain range of energy, the system can host a non-ergodic extended (i.e. metallic) phase in which the energy eigenstates violate the eigenstate thermalization hypothesis (ETH) but the entanglement entropy obeys volume-law scaling. The level statistics and entanglement growth also indicate the lack of ergodicity in these models. The phenomenon of localization and non-ergodicity in a system with interactions despite the presence of single-particle delocalized states is closely related to the so-called “many-body proximity effect” and can also be observed in models with disorder coupled to systems with delocalized degrees of freedom. Many-body localization in systems with incommensurate potentials (without single-particle mobility edges) have been realized experimentally, and we show how this can be modified to study the the effects of such mobility edges. Demonstrating the failure of thermalization in the presence of a single-particle mobility edge in the thermodynamic limit would indicate a more robust violation of the ETH.Delocalized states conventionally act as reservoirs for localized ones in systems with interactions. However, this may not be true for models with incommensurate potentials with single particle mobility edges. Such systems can host a non-ergodic extended phase in which the many-body eigenstates are not thermal but have extensive entropy. The failure of thermalization in these systems may provide a stronger violation of the eigenstate thermalization hypothesis than in conventional many-body localization. PubDate: 2017-05-02T10:42:23.687103-05: DOI: 10.1002/andp.201600399

Authors:Richard Berkovits Abstract: Statistical properties of the low-lying states of the entanglement spectrum of a one-dimensional interacting disordered system are studied in order to understand the localized to extended transition as function of interaction strength and excitation number expected from the many-body localization transition. It is shown that such a transition is observed in the statistics of the level-spacing of the entanglement spectrum. For an intermediate range of excitation numbers and strong interaction strength where the entanglement spectrum shows a clear extended behavior, a signature of non-ergodic behavior also emerges. We interpret this as evidence for a non-ergodic-extended phase suggested by previous studies.The excitation statistics of low-lying levels of the entanglement spectrum is studied searching for a localized to extended transition as function of interaction and excitation number expected from the MBL transition. For a 1D disordered system we show that such a transition is observed. An intermediate range of excitation numbers and interaction strength appears where extended states coexist with non-ergodic behavior. This is interpreted as evidence for a non-ergodic-extended phase. PubDate: 2017-04-27T18:56:14.138277-05: DOI: 10.1002/andp.201700042

Authors:I. V. Gornyi; A. D. Mirlin, D. G. Polyakov, A. L. Burin Abstract: We analyze the role of spectral diffusion in the problem of many-body delocalization in quantum dots and in extended systems. The spectral diffusion parametrically enhances delocalization, modifying the scaling of the delocalization threshold with the interaction coupling constant.This paper analyzes the role of spectral diffusion in the problem of many-body delocalization in quantum dots and in extended systems. It is shown that the spectral diffusion parametrically enhances delocalization, modifying the scaling of the delocalization threshold with the interaction coupling constant. PubDate: 2017-04-27T18:55:15.13043-05:0 DOI: 10.1002/andp.201600360

Authors:Rajeev Singh; Efrat Shimshoni Abstract: Localization in interacting systems caused by disorder, known as many-body localization (MBL), has attracted a lot of attention in recent years. Most systems studied in this context also show single-particle localization, and the question of MBL is whether the phenomena survives the effects of interactions. It is intriguing to consider a system with no single-particle localization but which does localize in the presence of many particles. The localization phenomena occurs “due to” rather than “in spite of” interactions in such systems. We consider a simple bosonic system and show that interactions enhance the effects of very weak disorder and result in localization when many particles are present. We provide physical insights into the mechanism involved and support our results with analytical and numerical calculations.The phenomena of localization caused by strong disorder plays a very fundamental role in understanding the breakdown of thermalization in quantum systems. In this work it has been shown that for bosonic systems, interactions can enhance seemingly small disorder resulting in suppression of quantum fluctuations and emergence of localization. Analytical calculations highlight the role of finite disorder however small, as well as the onset of quantum behavior. PubDate: 2017-04-13T10:44:15.573096-05: DOI: 10.1002/andp.201600309

Authors:P. Prelovšek; M. Mierzejewski, O. Barišić, J. Herbrych Abstract: We present a review of recent theoretical results concerning the many-body localization (MBL) phenomenon, with the emphasis on dynamical density correlations and transport quantities. They are shown to be closely related, providing a comprehensive description of the ergodic-to-nonergodic transition, consistent with experimental findings. While the focus is set mostly on the one-dimensional model of interacting spinless fermions, we also present evidence for the absence of full MBL in the one-dimensional Hubbard model and for the density-wave decay induced by the inter-chain coupling.We present a review of recent theoretical results concerning the many-body localization phenomenon, with the emphasis on dynamical density correlations and transport quantities. The focus is on the results for the one-dimensional model of interacting spinless fermions, we also present evidence for the absence of full localization in the one-dimensional Hubbard model and for the density-wave decay induced by the inter-chain coupling. PubDate: 2017-04-11T06:20:56.248563-05: DOI: 10.1002/andp.201600362

Authors:Adrian Wüthrich Abstract: One of the first publications by the ATLAS collaboration using data from the Large Hadron Collider at CERN dealt with the measurement of the production cross section of the W boson. The collaboration “rediscovered” the W in order to, among other things, check whether the detector and analysis methods were working well. Originally, the discovery of the W had been announced in 1983 by the CERN management, referring mainly to work done by its UA1 collaboration. In both the discovery and the “rediscovery”, the convergence of two distinct sets of criteria of data selection was an important concern of the researchers. In 1983, this concern figured prominently in the published paper whereas in 2010 it was mainly dealt with inside the collaboration. PubDate: 2017-04-03T08:40:32.387199-05: DOI: 10.1002/andp.201700101

Authors:Carolyn Zhang; Frank Pollmann, S. L. Sondhi, Roderich Moessner Abstract: We generalize the recently introduced Density-Matrix Renormalization Group (DMRG-X) [Khemani et al, PRL 2016] algorithm to obtain Floquet eigenstates of one-dimensional, periodically driven many-body localized systems. This generalization is made possible by the fact that the time-evolution operator for a period can be efficiently represented using a matrix-product operator. We first benchmark the method by comparing to exact diagonalization for small systems. We then obtain Floquet eigenstates for larger systems and show unambiguously that the characteristic area-law scaling remains robust.Time-evolving block decimation and a modified density-matrix renormalization group [Khemani et al, PRL 2016] is applied to efficiently obtain Floquet eigenstates of one-dimensional, periodically driven many-body localized systems. Signatures of many-body localization such as area-law entanglement entropy remain robust over a range of parameters. A log- arithmic growth of the disorder averaged maximum entanglement entropy indicates the presence of resonant regions. PubDate: 2017-03-31T07:10:40.991586-05: DOI: 10.1002/andp.201600294

Authors:Konstantin G. Zloshchastiev Abstract: It is shown that quantum sustainability is a universal phenomenon which emerges during environment-assisted electronic excitation energy transfer (EET) in photobiological complexes (PBCs), such as photosynthetic reaction centers and centers of melanogenesis. We demonstrate that quantum photobiological systems must be sustainable for them to simultaneously endure continuous energy transfer and keep their internal structure from destruction or critical instability. These quantum effects occur due to the interaction of PBCs with their environment which can be described by means of the reduced density operator and effective non-Hermitian Hamiltonian (NH). Sustainable NH models of EET predict the coherence beats, followed by the decrease of coherence down to a small, yet non-zero value. This indicates that in sustainable PBCs, quantum effects survive on a much larger time scale than the energy relaxation of an exciton. We show that sustainable evolution significantly lowers the entropy of PBCs and improves the speed and capacity of EET.The work addresses a long-standing problem of quantum photobiology and UV-physiology: is there a universal mechanism, which would explain high efficiency and sustainability of energy transfer in otherwise completely different photobiological systems inside living organisms or organelles, such as photosynthetic reaction centers and centers of melanogenesis? It is shown that certain interactions of these systems with their environment facilitate energy transfer, preserve quantum coherence and reduce entropy. PubDate: 2017-03-30T06:20:46.923457-05: DOI: 10.1002/andp.201600185

Authors:D. Schulze; A. Thakur, A.S. Moskalenko, J. Berakdar Abstract: Single neutral atom mechanics is controllable by focused, high-intensity optical vortices. The intensity-dependent, laser-driven motion of the atom's active electrons subsumes to a net transfer of the orbital angular momentum of the light to the neutral atom. The ponderomotive force on these electrons translates so into an unbounded or a bounded radial drift of the atom depending on its initial kinetic energy, as set by the temperature. Appropriate combination of laser beams results in sub-wavelength, dynamical radial traps for tweezing atoms controllably, an effect that can be exploited for atom guiding, structuring, and lithographic applications.Intense optical vortices work together to fling neutral atoms with trillions the earth accelerations. The vortex pulses can be tailored to form traps and move the atoms gently in ferris wheel thousands of times larger than the residual atom. The approach is relevant for applications for neutral atoms guiding, stacking and structuring, and in sub-optical wavelength lithography. PubDate: 2017-03-27T13:15:46.008953-05: DOI: 10.1002/andp.201600379

Authors:Michael Schecter; Michael Shapiro, Mark I. Dykman Abstract: We show that, in a many-body system, all particles can be strongly confined to the initially occupied sites for a time that scales as a high power of the ratio of the bandwidth of site energies to the hopping amplitude. Such time-domain formulation is complementary to the formulation of the many-body localization of all stationary states with a large localization length. The long localization lifetime is achieved by constructing a periodic sequence of site energies with a large period in a one-dimensional chain. The scaling of the localization lifetime is independent of the number of particles for a broad range of the coupling strength. The analytical results are confirmed by numerical calculations.How long can strongly interacting particles stay almost entirely confined to the sites they initially occupied? Unexpectedly, a long confinement time can be achieved for a periodic sequence of site energies. A “magic” period is 6. For such a period, judiciously constructed site energies lead to the confinement for times that scale as (h/J)5 in a broad range of the particle-particle interaction V. PubDate: 2017-03-27T13:15:39.864567-05: DOI: 10.1002/andp.201600366

Authors:Louk Rademaker; Miguel Ortuño, Andres M. Somoza Abstract: We study many-body localization (MBL) from the perspective of integrals of motion (IOMs). MBL can be understood phenomenologically through the existence of macroscopically many localized IOMs. We develop a systematic procedure based on IOM to calculate many-body quantities. Displacement transformations made clear that any operator can be expanded in 1-,2- ... n-particles terms. We use this property to develop a systematic procedure to approximately calculate IOMs and many-body quantities. We characterize the decay with distance of the IOM's and their interactions through effective localization lengths. For all values of disorder the typical IOMs are localized, suggesting the importance of rare fluctuations in understanding the MBL-to-ergodic transition.Many-body localization can be understood through the existence of macroscopically many localized integrals of motion. We develop a systematic procedure to calculate integrals of motion and many-body quantities. We characterize their decay with distance and their interactions through effective localization lengths. An analysis of the coefficients of the integrals of motion suggests the importance of rare fluctuations in understanding the many-body localization problem. PubDate: 2017-03-27T01:45:43.952322-05: DOI: 10.1002/andp.201600322

Authors:Houssam Abdul-Rahman; Bruno Nachtergaele, Robert Sims, Günter Stolz Abstract: We review several aspects of Many-Body Localization-like properties exhibited by the disordered XY chains: localization properties of the energy eigenstates and thermal states, propagation bounds of Lieb-Robinson type, decay of correlation functions, absence of particle transport, bounds on the bipartite entanglement, and bounded entanglement growth under the dynamics. We also prove new results on the absence of energy transport and Fock space localization. All these properties are made accessible to mathematical analysis due to the exact mapping of the XY chain to a system of quasi-free fermions given by the Jordan-Wigner transformation. Motivated by these results we discuss conjectured properties of more general disordered quantum spin and other systems as possible directions for future mathematical research.Zero-velocity Lieb-Robinson bounds, describing the absence of information transport, are arising as one of the characteristics of the many-body localized phase in disordered quantum spin systems. These bounds and other many-body localization properties, including exponential clustering and area laws for the bipartite entanglement of eigenstates at arbitrary energy, can be proven rigorously for the disordered XY chain. PubDate: 2017-03-24T03:10:58.280078-05: DOI: 10.1002/andp.201600280

Authors:R. Daneshmand; M. K. Tavassoly Abstract: Recently the quantum description of electromagnetic waves in conducting media has been performed. It has been deduced that, in particular situations the Hamiltonian of corresponding field can be expressed by the well-known Caldirola-Kanai Hamiltonian. In this paper, using the associated annihilation and creation operators of the above-mentioned real physical system, a few schemes for the generation of some classes of time-dependent multipartite entangled coherent squeezed states are proposed. To achieve the purpose, the interaction of a narrow bunch of two-level atoms with such a quantized field in a conducting cavity and in the presence of a strong-driving classical field is taken into account. The influence of the conductivity parameter on the degree of entanglement and atomic population inversion is studied, numerically. As will be clarified, the related physical quantities can be controlled by the conductivity parameter. In detail, it is shown that the entanglement reaches to its maximum value with smaller delay in the presence of larger values of conductivity. Also, it is observed that by increasing the conductivity, the time for occurring collapse-revival in the atomic inversion is decreased.The Hamiltonian of electromagnetic waves in conducting media has been expressed by Caldirola-Kanai Hamiltonian. Using this formalism, the interaction of a narrow bunch of two-level atoms with such a quantized field in the presence of a strong-driving classical field is considered. The time-dependent multipartite entangled coherent squeezed states are generated, and the population inversion (linear entropy) is evaluated, where it is observed that the collapse-revivals (degree of entanglement) can be controlled by the conductivity parameter. PubDate: 2017-03-24T03:05:48.427276-05: DOI: 10.1002/andp.201600246

Authors:Yuliya S. Dadoenkova; Sergey G. Moiseev, Aleksei S. Abramov, Aleksei S. Kadochkin, Andrei A. Fotiadi, Igor O. Zolotovskii Abstract: A mechanism of amplification of surface plasmon polaritons due to the transfer of electromagnetic energy from a drift current wave into a far-infrared surface wave propagating along a semiconductor-dielectric boundary in waveguide geometry is proposed. A necessary condition of the interaction of these waves is phase matching condition, i. e., when the phase velocity of the surface wave approaches the drift velocity of charge carriers. It is shown that in the spectral region of the surface plasmon polariton slowing-down its amplification coefficient can reach values substantially exceeding the ohmic loss coefficient of the surface wave in the structure.A slow surface plasmon polariton propagating in the semiconductor film – graphene monolayer – dielectric structure is shown to be amplified by electric current in graphene. Effect of the amplification appears due to the energy transferring from direct electric current to surface plasmon-polariton. The amplification coefficient can up to three orders of magnitude exceed the loss coefficient of a surface plasmon polariton. PubDate: 2017-03-24T03:05:38.209835-05: DOI: 10.1002/andp.201700037

Authors:Alexandros Chremos; Jack F. Douglas Abstract: The properties of materials largely reflect the degree and character of the localization of the molecules comprising them so that the study and characterization of particle localization has central significance in both fundamental science and material design. Soft materials are often comprised of deformable molecules and many of their unique properties derive from the distinct nature of particle localization. We study localization in a model material composed of soft particles, hard nanoparticles with grafted layers of polymers, where the molecular characteristics of the grafted layers allow us to “tune” the softness of their interactions. Soft particles are particular interesting because spatial localization can occur such that density fluctuations on large length scales are suppressed, while the material is disordered at intermediate length scales; such materials are called “disordered hyperuniform”. We use molecular dynamics simulation to study a liquid composed of polymer-grafted nanoparticles (GNP), which exhibit a reversible self-assembly into dynamic polymeric GNP structures below a temperature threshold, suggesting a liquid-gel transition. We calculate a number of spatial and temporal correlations and we find a significant suppression of density fluctuations upon cooling at large length scales, making these materials promising for the practical fabrication of “hyperuniform” materials.Many of the unique properties of soft materials derive from the way the molecules localize from their packing interactions. Particle deformability allows new particle localization states at which the density fluctuations are greatly suppressed, like in crystals, while being disordered; such materials are called “disordered hyperuniform”. A promising material with such properties is a liquid composed of polymer-grafted nanoparticles that exhibits a reversible liquid-gel transition. PubDate: 2017-03-23T02:35:35.665773-05: DOI: 10.1002/andp.201600342

Authors:Asmi Haldar; Arnab Das Abstract: Quantum interference lies at the heart of several surprising equilibrium and non-equilibrium phenomena in many-body Physics. Here we discuss two recently explored non-equilibrium scenarios where external periodic drive applied to closed (i.e., not attached to any external bath) quantum many-body systems have apparently opposite effects in respective cases. In one case it freezes/localizes a disorder free system dynamically, while in the other it delocalizes a disordered many-body localized system, and quantum interference is responsible for both the effects. We review these in the perspective of more general questions of ergodicity, energy absorption, asymptotic behavior, and finally the essential role of quantum mechanics in understanding these issues in periodically driven closed many-body systems. In this article we intend to deliver a non-technical account of some recent developments in this field in a manner accessible to a broad readership.Periodic drive can induce both localization and delocalization in many-body quantum systems. Free systems can undergo Dynamical Many-body Freezing (freezing of population dynamics for all degrees of freedom) under periodic drive (upper line: freeing of transverse magnetization in a transverse field Ising chain), while an originally Many-body Localized system can be delocalized completely under periodic drive (lower line: flat Eigenstate Expectation Values vs Floquet quasienergies of an onsite occupation number). PubDate: 2017-03-21T05:11:55.305211-05: DOI: 10.1002/andp.201600333

Authors:Peter Schlagheck; Julien Dujardin Abstract: We present numerical evidence for the occurrence of coherent backscattering in the Fock space of a small disordered Bose-Hubbard system consisting of four sites and containing five particles. This many-body interference phenomenon can most conveniently be seen in time evolution processes that start from a Fock state of the Bose-Hubbard system. It manifests itself in an enhanced detection probability of this initial state as compared to other Fock states with comparable total energy. We argue that coherent backscattering in Fock space can be experimentally measured with ultracold bosonic atoms in optical lattices using state-of-the-art single-site detection techniques. A synthetic gauge field can be induced in order to break time-reversal symmetry within the lattice and thereby destroy coherent backscattering. While this many-body interference effect is most prominently visible in the presence of eigenstate thermalization, we briefly discuss its significance in the opposite regime of many-body localization.A quantum many-body system that is prepared in a specific Fock state with respect to a single-particle basis has an enhanced probability to come back to this initial state in the course of time evolution as compared to other Fock states with comparable energy. This effect arises due to coherent backscattering in Fock space. It can be probed using ultracold bosonic atoms in optical lattices. PubDate: 2017-03-21T05:11:21.087483-05: DOI: 10.1002/andp.201600311

Authors:Alexander Burin Abstract: The analytical solution of a many-body localization problem in a quantum Sherrington-Kirkpatrick spin glass model in a random longitudinal field is proposed matching the problem with a model of Anderson localization in a Bethe lattice. The localization transition is dramatically sensitive to the relationship between interspin interaction and random field revealing different regimes in which the interaction can either suppress or enhance the delocalization. The localization is enhanced by decreasing the temperature and the localization transition shows a remarkable universality in a spin glass phase. The observed trends should be qualitatively relevant for other systems showing many-body localization.Analytical solution is developed for many-body localization in a quantum spin glass model with an infinite range spin-spin binary interaction using a matching localization problem on a Bethe lattice that can be solved exactly. The dependencies of localization threshold on random fields, interaction and temperature are determined in this model and similar behaviors are expected in more realistic settings. PubDate: 2017-03-21T04:50:23.889449-05: DOI: 10.1002/andp.201600292

Authors:Salvatore Capozziello; Maurizio Capriolo, Maria Transirico Abstract: We derive the gravitational energy momentum tensor ταη for a general Lagrangian of any order L=L(gμν,gμν,i1,gμν,i1i2,gμν,i1i2i3,⋯,gμν,i1i2i3⋯in) and in particular for a Lagrangian such as Lg=(R¯+a0R2+∑k=1pakR□kR)−g. We prove that this tensor, in general, is not covariant but only affine, then it is a pseudo-tensor. Furthermore, the pseudo-tensor ταη is calculated in the weak field limit up to a first non-vanishing term of order h2 where h is the metric perturbation. The average value of the pseudo-tensor over a suitable spacetime domain is obtained. Finally we calculate the power per unit solid angle Ω carried by a gravitational wave in a direction x̂ for a fixed wave number k under a suitable gauge. These results are useful in view of searching for further modes of gravitational radiation beyond the standard two modes of General Relativity and to deal with nonlocal theories of gravity where terms involving □R are present. The general aim of the approach is to deal with theories of any order under the same standard of Landau pseudo-tensor.The gravitational enenergy-momentum tensor is related to the transport properties of gravitational waves. In this paper, it has been derived for metric theories of gravity of any derivative order pointing out further gravitational polarizations modes and non-locality properties. These features could be extremely relevant in view of Quantum Gravity and gravitational waves detection. PubDate: 2017-03-15T10:05:44.926545-05: DOI: 10.1002/andp.201600376

Authors:Yaser Tavakoli; Celia Escamilla-Rivera, Júlio C. Fabris Abstract: In this paper, we address the implications when a homogeneous dust model is considered for a scenario of gravitational collapse in the context of Eddington-inspired Born-Infeld (EiBI) theory. In order to describe the dynamical evolution of the collapse, we present an effective equation, which constitutes the first order corrections, in EiBI coupling parameter κ, to Einstein's field equations. The geometry outside the collapsing object is derived by imposing the standard Darmois-Israel junction conditions at the boundary surface of the dust. This induces an effective matter source in the outer region which gives rise to a non-singular, non-Schwarzschild geometry at the final state of the collapse. For this exterior geometry, we find the threshold of mass for the formation of the black hole. This provides a cut-off over κ as κ =5.1×10−97kg−1·m3.Black holes are solutions of the General Relativity (GR) theory containing a “singularity” at its center covered by “event horizon”. The “Eddington-inspired Born-Infeld” (EiBI) theory, as an alternative to GR, keeps many of the properties of GR, but creating conditions to avoid its undesirable features: it implies that, in a dust collapse, the central singularity is resolved, and there exists a threshold mass for formation of a non-Schwarzschild black hole. PubDate: 2017-03-13T02:25:32.717711-05: DOI: 10.1002/andp.201600415

Authors:He-Xiu Xu; Shiwei Tang, Xiaohui Ling, Weijie Luo, Lei Zhou Abstract: Achieving flexible and highly directive emissions toward pre-designed directions has intrigued long-held interest in both science and engineering community, but most available efforts suffer the issues of bulky size, limited functionalities, and low efficiency. Here, we propose a general strategy to efficiently and flexibly control the emission beams with dual functionalities realized independently by orthogonal excitations. To overcome the polarization cross-talking, a novel planar multi-mode anisotropic meta-atom is designed by incorporating the screening effect of a surrounding wire loop. As the result, we can design the polarization-dependent phase profile under certain polarization, without worrying about their influences on the other polarization. As an illustration, two proof-of-concept metasurfaces are actualized at microwave frequencies, of which one combines the functionalities of focused-beam and large-angle multibeam emissions while another hybrids the functionalities of beam-steering and small-angle multibeam emissions. Theoretical, full-wave simulation, and experimental results are in excellent agreement with each other, which collectively demonstrate the desired performances of our bifunctional devices. Our proposed strategy paves the way to realize high-performance multifunctional optical devices with high integration and complex wavefront manipulations.Flexible control on directive emissions toward pre-designed directions has attracted long-term interest, but available devices suffer from bulky size, limited functionalities, and low efficiencies. Here, a novel anisotropic meta-atom exhibiting low polarization cross-talking was proposed, based on which high-efficiency metasurfaces with arbitrary polarization-dependent phase profiles can be easily designed to realize desired beam-control functionalities. The strategy paves the way to realize high-performance multifunctional optical devices with high integration. PubDate: 2017-03-10T10:53:37.680478-05: DOI: 10.1002/andp.201700045

Authors:Yuchen Xu; Hao Zhang, Yujun Lin, Heyuan Zhu Abstract: Spatially inhomogeneous disorder exists widely in optical systems. We present a numerical study on the light transport properties and analysis of transmission channels in random media with inhomogeneous disorder. For the case of longitudinal inhomogeneity of disorder we find that the statistics of the transmission channels is independent of the inhomogeneity and the system can be equivalent to a counterpart with homogeneous disorder strength, both of which have the same statistical distribution of the transmission channels. However, for the case of transverse inhomogeneity of disorder, such equivalence does not exist. The distribution of the total transmission is broadened and one most transmitted incident channel emerges.The present work investigates the light transmission properties in disordered samples with inhomogeneous disorder geometries. The equivalence in the case of longitudinal inhomogeneous disorder is verified while such equivalence cannot be found in the case of transversely inhomogeneous disorder. Moreover, in the case of transverse disorder geometry, a most transmitted incident channel emerges as shown in the figure. PubDate: 2017-03-10T10:27:43.391495-05: DOI: 10.1002/andp.201600225

Authors:Minglun Mo; Jing Wang, Yunan Wu Abstract: Evolution speed of an open quantum system is vividly influenced by the structure of environments. The strong system-environment coupling is found to be able to accelerate quantum evolution. In this work, we propose a different method of governing the quantum speedup via engineering multiple environments. It is shown that, with a judicious choice of the number of coupling environments, the quantum speedup of an open system can be achieved even under weak system-environment coupling conditions. The mechanism for the speedup is due to the switch between Markovian and non-Markovian regions by manipulating the number of the surrounding environments. In addition, we verify the above phenomena by using quantum dots embedded in a planar photonic crystal under current technologies. These results provide a new degree of freedoms to accelerate quantum evolution of open systems. The strong system-environment coupling can speed up the quantum evolution process. This work shows that, via engineering multiple environments, one can speed up the evolution process even under weak coupling conditions.The strong system-environment coupling can speed up the quantum evolution process. This work shows that, via engineering multiple environments, one can speed up the evolution process even under weak coupling conditions. PubDate: 2017-03-10T10:26:18.5691-05:00 DOI: 10.1002/andp.201600221

Authors:N. D. Chavda; V. K. B. Kota Abstract: Localization to delocalization transitions in eigenfunctions are studied for finite interacting boson systems by employing one- plus two-body embedded Gaussian orthogonal ensemble of random matrices [EGOE(1+2)]. In the first analysis, considered are bosonic EGOE(1+2) for two-species boson systems with a fictitious (F) spin degree of freedom [called BEGOE(1+2)-F]. Numerical calculations are carried out as a function of the two-body interaction strength (λ). It is shown that, in the region (defined by λ>λc) after the onset of Poisson to GOE transition in energy levels, the strength functions exhibit Breit-Wigner to Gaussian transition for λ>λFk>λc. Further, analyzing information entropy and participation ratio, it is established that there is a region defined by λ∼λt where the system exhibits thermalization. The F-spin dependence of the transition markers λFk and λt follow from the propagator for the spectral variances. These results, well tested near the center of the spectrum and extend to the region within ±2σ to ±3σ from the center (σ2 is the spectral variance), establish universality of the transitions generated by embedded ensembles. In the second analysis, entanglement entropy is studied for spin-less BEGOE(1+2) ensemble and shown that the results generated are close to the recently reported results for a Bose-Hubbard model.Universality of the localizaton-delocalization transitions generated by embedded random interaction matrix ensembles is established by showing that the ensembles for two species boson systems with a fictitious spin-1/2 degree of freedom, generate three transition markers. The third marker defines a region of thermalization. Also for the first time, the bipartite entanglement entropy is studied using embedded ensembles for spin-less boson systems and shown that the results are close to those obtained recently using Bose-Hubbard models. PubDate: 2017-03-09T09:05:43.170199-05: DOI: 10.1002/andp.201600287

Authors:Dario Bercioux; Omjyoti Dutta, Enrique Rico Abstract: We investigate the spectral properties of a quasi-one-dimensional lattice in two possible dimerisation configurations. Both configurations are characterised by the same lattice topology and the identical spectra containing a flat band at zero energy. We find that, one of the dimerised configuration has similar symmetry to a one-dimensional chain proposed by Su-Schrieffer-Heeger for studying solitons in conjugated polymers. Whereas, the other dimerised configuration only shows non-trivial topological properties in the presence of chiral-symmetry breaking adiabatic pumping.We study an enlarged version of the popular SSH model for studying solitons in polyacetylene. Our system allows for two possible dimerized phases. We show that one of the two is a higher dimensional representation of the SSH model, whereas the second one is a trivial representation that does not show any topological phase. PubDate: 2017-03-08T03:15:44.38263-05:0 DOI: 10.1002/andp.201600262

Authors:Zhongkai Huang; Lipeng Chen, Nengji Zhou, Yang Zhao Abstract: Following the Dirac-Frenkel time-dependent variational principle, transient dynamics of a one-dimensional Holstein polaron with diagonal and off-diagonal exciton-phonon coupling in an external electric field is studied by employing the multi-D2 Ansatz, also known as a superposition of the usual Davydov D2 trial states. Resultant polaron dynamics has significantly enhanced accuracy, and is in perfect agreement with that derived from the hierarchy equations of motion method. Starting from an initial broad wave packet, the exciton undergoes typical Bloch oscillations. Adding weak exciton-phonon coupling leads to a broadened exciton wave packet and a reduced current amplitude. Using a narrow wave packet as the initial state, the bare exciton oscillates in a symmetric breathing mode, but the symmetry is easily broken by weak coupling to phonons, resulting in a non-zero exciton current. For both scenarios, temporal periodicity is unchanged by exciton-phonon coupling. In particular, at variance with the case of an infinite linear chain, no steady state is found in a finite-sized ring within the anti-adiabatic regime. For strong diagonal coupling, the multi-D2 Anstaz is found to be highly accurate, and the phonon confinement gives rise to exciton localization and decay of the Bloch oscillations.Following the Dirac-Frenkel time-dependent variational principle, transient dynamics of a one-dimensional Holstein polaron with diagonal and off-diagonal exciton-phonon coupling in an external field is studied by employing the multi-D2 Ansatz. In the anti-adiabatic regime, the temporal periodicity of the Bloch oscillations survives the introduction of the exciton-phonon coupling, while their spatial periodicity is lost. Strong diagonal coupling leads to damped oscillations of the exciton current in a strong field. PubDate: 2017-03-02T02:40:39.041458-05: DOI: 10.1002/andp.201600367

Authors:François Huveneers Abstract: We review possible mechanisms for energy transfer based on ‘rare’ or ‘non-perturbative’ effects, in physical systems that present a many-body localized phenomenology. The main focus is on classical systems, with or without quenched disorder. For non-quantum systems, the breakdown of localization is usually not regarded as an issue, and we thus aim at identifying the fastest channels for transport. Next, we contemplate the possibility of applying the same mechanisms in quantum systems, including disorder free systems (e.g. Bose-Hubbard chain), disordered many-body localized systems with mobility edges at energies below the edge, and strongly disordered lattice systems in d>1. For quantum mechanical systems, the relevance of these considerations for transport is currently a matter of debate.In this feature article, the author reviews some recent progress in the understanding of the MBL phase. The focus is on the role of rare ergodic spots that can potentially harm the stability of the localized phase. Such spots naturally occur through local inclusions of the thermal phase in the localized phase, which are unavoidable in any realistic interacting system, due to either thermal fluctuations or disorder fluctuations. PubDate: 2017-03-02T02:40:30.514173-05: DOI: 10.1002/andp.201600384

Authors:Luca Dell'Anna Abstract: We provide and study complete sets of one-loop renormalization group equations of several Finkel'stein non-linear σ models, the effective field theories describing the diffusive quantum fluctuations in correlated disordered systems. We consider different cases according to the presence of certain symmetries induced by the original random Hamiltonians, and we show that, for interacting systems, the Cartan's classification of symmetry classes is not enough to uniquely determine their scaling behaviors.The study of the interplay beteen disorder and interactions, which is the origin of still unclear phenomena in electron systems, is a challenging task for modern condensed matter physicists. One of the most powerful and versatile tool to deal with disordered correlated fermions is the non-linear sigma-model approach, which takes into account the symmetry properties of different random systems allowing for a systematic study in terms of symmetry classes. PubDate: 2017-02-28T05:11:17.942242-05: DOI: 10.1002/andp.201600317

Authors:Douglas M. Photiadis Abstract: Starting from a continuum description of a disordered elastic medium, we have derived a supersymmetric field theoretic model enabling the prediction of ensemble average correlation functions that fully takes polarization effects into account. The model enables both perturbative and non-perturbative calculations in a similar fashion as corresponding models of disordered electronic systems. At intermediate distances, we show that a Hubbard-Stratonovic transformation can be carried out and obtain a supermatrix field theory. At distances far greater than the mean free paths of the system, we show that the action reduces to a nonlinear supersymmetric sigma model formally identical to that for a scalar field. Our results yield a bare diffusion constant given by a density of states weighted average of the classical diffusion constants of the coherent potential approximation(CPA) medium.The transport of vibrational energy in disordered solids is important across a broad range of physical systems. While much progress has been made, a full theoretical description of such systems has yet to be given, particularly with regard to the interference phenomena leading to enhanced backscattering and localization effects. This article presents a theoretical advance enabling a fuller and more accurate description of such phenomena. PubDate: 2017-02-27T06:50:58.467875-05: DOI: 10.1002/andp.201600353

Authors:I. V. Gornyi; A. D. Mirlin, M. Müller, D. G. Polyakov Abstract: We consider an extended electronic system with localized single-particle states coupled by short-range interactions, in the absence of coupling to an external bath. We show that many-body localization, which exists in tight-binding models, is unstable in a continuum. Irrespective of the dimensionality of the system, many-body localization does not survive the unbounded growth of the single-particle localization length with increasing energy that is characteristic of the continuum limit. The system remains delocalized down to arbitrarily small temperature T, although its dynamics slows down as T decreases. Remarkably, the conductivity vanishes with decreasing T faster than in the Arrhenius law. The system can be characterized by an effective T-dependent single-particle mobility edge which diverges in the limit of T0. Delocalization is driven by interactions between hot electrons above the mobility edge and the “bath” of thermal electrons in the vicinity of the Fermi level.It is shown that many-body localization does not survive in a continuum, since high-energy excitations form a weak delocalized bath. In dimensions d=1 and 2, instead of super-insulation one finds a regime of low-temperature transport with a resistivity that increases in a super-Arrhenius fashion. The latter is identified as a key hallmark of systems as close as possible to being many-body localized. PubDate: 2017-02-14T08:25:36.981453-05: DOI: 10.1002/andp.201600365

Authors:David Fischer; Sandro Wimberger Abstract: We discuss the relaxation dynamics for a bosonic tunneling junction with two modes in the central potential well. We use a master equation description for ultracold bosons tunneling in the presence of noise and incoherent coupling processes into the two central modes. Whilst we cannot quantitatively reproduce the experimental data of the setup reported in [Phys. Rev. Lett. 115, 050601 (2015)], we find a reasonable qualitative agreement of the refilling process of the initially depleted central site. Our results may pave the way for the control of bosonic tunneling junctions by the simultaneous presence of decoherence processes and atom-atom interaction.The relaxation dynamics are studied for a bosonic tunneling junction with two modes in the central potential well. The importance of incoherent processes in the refilling of the initially depleted central site is shown and qualitative agreement with recent experimental results is obtained. PubDate: 2017-02-13T05:55:54.775068-05: DOI: 10.1002/andp.201600327

Authors:Sheldon Goldstein; David A. Huse, Joel L. Lebowitz, Roderich Tumulka Abstract: We study the nature of and approach to thermal equilibrium in isolated quantum systems. An individual isolated macroscopic quantum system in a pure or mixed state is regarded as being in thermal equilibrium if all macroscopic observables assume rather sharply the values obtained from thermodynamics. Of such a system (or state) we say that it is in macroscopic thermal equilibrium (MATE). A stronger requirement than MATE is that even microscopic observables (i.e., ones referring to a small subsystem) have a probability distribution in agreement with that obtained from the micro-canonical, or equivalently the canonical, ensemble for the whole system. Of such a system we say that it is in microscopic thermal equilibrium (MITE). The distinction between MITE and MATE is particularly relevant for systems with many-body localization (MBL) for which the energy eigenfuctions fail to be in MITE while necessarily most of them, but not all, are in MATE. However, if we consider superpositions of energy eigenfunctions (i.e., typical wave functions ψ) in an energy shell, then for generic macroscopic systems, including those with MBL, most ψ are in both MATE and MITE. We explore here the properties of MATE and MITE and compare the two notions, thereby elaborating on ideas introduced in .In quantum mechanics, there are two types of thermal equilibrium, and their difference is particularly relevant to systems with many-body localization: In the first and basic type, all macroscopic observables assume rather sharply their equilbrium values. A second and stronger type, but still valid for most states, is that even microscopic observables are distributed according to their thermal equilibrium distribution. PubDate: 2017-02-09T02:20:50.063585-05: DOI: 10.1002/andp.201600301

Authors:Soumya Bera; Thomas Martynec, Henning Schomerus, Fabian Heidrich-Meisner, Jens H. Bardarson Abstract: We study interacting fermions in one dimension subject to random, uncorrelated onsite disorder, a paradigmatic model of many-body localization (MBL). This model realizes an interaction-driven quantum phase transition between an ergodic and a many-body localized phase, with the transition occurring in the many-body eigenstates. We propose a single-particle framework to characterize these phases by the eigenstates (the natural orbitals) and the eigenvalues (the occupation spectrum) of the one-particle density matrix (OPDM) in individual many-body eigenstates. As a main result, we find that the natural orbitals are localized in the MBL phase, but delocalized in the ergodic phase. This qualitative change in these single-particle states is a many-body effect, since without interactions the single-particle energy eigenstates are all localized. The occupation spectrum in the ergodic phase is thermal in agreement with the eigenstate thermalization hypothesis, while in the MBL phase the occupations preserve a discontinuity at an emergent Fermi edge. This suggests that the MBL eigenstates are weakly dressed Slater determinants, with the eigenstates of the underlying Anderson problem as reference states. We discuss the statistical properties of the natural orbitals and of the occupation spectrum in the two phases and as the transition is approached. Our results are consistent with the existing picture of emergent integrability and localized integrals of motion, or quasiparticles, in the MBL phase. We emphasize the close analogy of the MBL phase to a zero-temperature Fermi liquid: in the studied model, the MBL phase is adiabatically connected to the Anderson insulator and the occupation-spectrum discontinuity directly indicates the presence of quasiparticles localized in real space. Finally, we show that the same picture emerges for interacting fermions in the presence of an experimentally-relevant bichromatic lattice and thereby demonstrate that our findings are not limited to a specific model.In finite quantum systems, interactions and disorder often work complementary. We provide a bridge between the clearly observable effects for individual particles and the collective many-body behavior, obtained by inspecting the shape and occupation of natural single-particle orbitals. Beyond a certain disorder strength, particles in these orbitals become spatially confined and the occupations well defined. This phenomenology aligns well with the transition to a many-body-localised phase. PubDate: 2017-02-06T01:45:53.796913-05: DOI: 10.1002/andp.201600356

Authors:S. A. Parameswaran; Andrew C. Potter, Romain Vasseur Abstract: We review recent advances in understanding the universal scaling properties of non-equilibrium phase transitions in non-ergodic disordered systems. We discuss dynamical critical points (also known as eigenstate phase transitions) between different many-body localized (MBL) phases, and between MBL and thermal phases.Disordered quantum systems open the door to new dynamical phase transitions far from thermal equilibrium. PubDate: 2017-01-20T06:25:49.234482-05: DOI: 10.1002/andp.201600302

Authors:E. J. Torres-Herrera; Lea F. Santos Abstract: This work supports the existence of extended nonergodic states in the intermediate region between the chaotic (thermal) and the many-body localized phases. These states are identified through an extensive analysis of static and dynamical properties of a finite one-dimensional system with onsite random disorder. The long-time dynamics is particularly sensitive to changes in the spectrum and in the structures of the eigenstates. The study of the evolution of the survival probability, Shannon information entropy, and von Neumann entanglement entropy enables the distinction between the chaotic and the intermediate region.Despite the consensus that the transition from a metal to an insulator can still take place in quantum systems with many interacting particles, the details are not entirely understood. It has been debated, for instance, whether there is an intermediate phase between the chaotic and the many-body localized phase. Our results for the long-time evolution of the survival probability makes clear the existence of the intermediate region. PubDate: 2017-01-13T14:15:40.242054-05: DOI: 10.1002/andp.201600284

Authors:Kartiek Agarwal; Ehud Altman, Eugene Demler, Sarang Gopalakrishnan, David A. Huse, Michael Knap Abstract: The low-frequency response of systems near the many-body localization phase transition, on either side of the transition, is dominated by contributions from rare regions that are locally “in the other phase”, i.e., rare localized regions in a system that is typically thermal, or rare thermal regions in a system that is typically localized. Rare localized regions affect the properties of the thermal phase, especially in one dimension, by acting as bottlenecks for transport and the growth of entanglement, whereas rare thermal regions in the localized phase act as local “baths” and dominate the low-frequency response of the MBL phase. We review recent progress in understanding these rare-region effects, and discuss some of the open questions associated with them: in particular, whether and in what circumstances a single rare thermal region can destabilize the many-body localized phase.The many-body localization transition demarcates quantum phases of matter that are remarkably different in their entanglement structure, response, and dynamical properties. Near the transition, this difference plays a significant role as rare inclusions of the opposite phase strongly modify the properties of the bulk, ‘enabling’ the transition, but also giving rise to a new ‘Griffiths’ phase with entirely novel dynamical characteristics. This review reflects the current understanding of such ‘Griffiths’ effects on the many-body localization transition. PubDate: 2017-01-12T13:30:54.653485-05: DOI: 10.1002/andp.201600326

Authors:Xiao Chen; Tianci Zhou, David A. Huse, Eduardo Fradkin Abstract: We use the out-of-time-order (OTO) correlators to study the slow dynamics in the many-body localized (MBL) phase. We investigate OTO correlators in the effective (“l-bit”) model of the MBL phase, and show that their amplitudes after disorder averaging approach their long-time limits as power-laws of time. This power-law dynamics is due to dephasing caused by interactions between the localized operators that fall off exponentially with distance. The long-time limits of the OTO correlators are determined by the overlaps of the local operators with the conserved l-bits. We demonstrate numerically our results in the effective model and three other more “realistic” spin chain models. Furthermore, we extend our calculations to the thermal phase and find that for a time-independent Hamiltonian, the OTO correlators also appear to vanish as a power law at long time, perhaps due to coupling to conserved densities. In contrast, we find that in the thermal phase of a Floquet spin model with no conserved densities the OTO correlator decays exponentially at long times.This paper studies the power law decay of out-of-time-order correlator in many body localized phases. This power law decay is verified in effective “l-bit” model and several disordered spin chain models. In addition, the calculation is also extended to the thermal phase. PubDate: 2016-12-26T23:50:38.353292-05: DOI: 10.1002/andp.201600332

Authors:Amalia Torre; Ambra Lattanzi, Decio Levi Abstract: A detailed study of the splinless (1+1)D free-particle Salpeter equation is presented. It involves several aspects of the topic: from the analysis of the behavior of solutions of the equation, both numerically evaluated and asymptotically approximated for definite initial conditions, to the comparison with the behavior of the corresponding solutions of the Schrödinger equation in order to both highlight the differences and to possibly understand how the latter “flow” in the former. Interesting analogies with other fields of physics, in particular with optics, are suggested.An accurate study of the spinless (1+1)D free-particle Salpeter equation is presented through the analysis of the behavior of definite solutions of the equation. Peculiar features of the evolution under the Salpeter equation are drawn out and explained in relation also with the geometry of the (1+1)D Minkowski space-time. Initial conditions, highlighting such features in connection with their “degree of localization”, are considered. Interesting analogies with other fields of physics are suggested. PubDate: 2016-12-19T04:02:39.43752-05:0 DOI: 10.1002/andp.201600231

Authors:Marko Žnidarič; Juan Jose Mendoza-Arenas, Stephen R. Clark, John Goold Abstract: We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime when bulk dephasing is present. We find that while dephasing always renders the transport diffusive, there is nonetheless a remnant of the diffusive to sub-diffusive transition found in a system without dephasing manifested in the behaviour of the diffusion constant with the dephasing strength. By studying finite-size effects we show numerically and theoretically that this feature is caused by the competition between large crossover length scales associated to disorder and dephasing that control the dynamics observed in the thermodynamic limit. We demonstrate that this competition may lead to a dephasing enhanced transport in this model.Transport in one-dimensional systems is strongly inflenced by disorder. Depending on disorder strength, one can have different phases displaying anomalous, diffusive, or insulating behavor. We study how such transport is modified by the coupling to the environment, showing that it always becomes diffusive, though with a remnant of clean phase transitions being imprinted in the dependence of the diffusion constant on the dephasing strength. PubDate: 2016-12-13T07:25:32.757887-05: DOI: 10.1002/andp.201600298

Authors:Vieri Mastropietro Abstract: Interacting spinning fermions with strong quasi-random disorder are analyzed via rigorous Renormalization Group (RG) methods combined with KAM techniques. The correlations are written in terms of an expansion whose convergence follows from number-theoretical properties of the frequency and cancellations due to Pauli principle. A striking difference appears between spinless and spinning fermions; in the first case there are no relevant effective interactions while in presence of spin an additional relevant quartic term is present in the RG flow. The large distance exponential decay of the correlations present in the non interacting case, consequence of the single particle localization, is shown to persist in the spinning case only for temperatures greater than a power of the many body interaction, while in the spinless case this happens up to zero temperature.A rigorous analysis of interacting spinning fermions with strong quasi-random Aubry-Andre' disorder is performed. The main difficult is posed by the appearance of small divisors (similar to the ones present in KAM theory) in a truly interacting quantum theory.The large distance exponential decay of correlations, consequence of the single particle localization, persists in the interacting spinning case only for temperatures greater than a power of the many body interaction, while in the spinless case this happens up to zero temperature. PubDate: 2016-12-09T14:30:44.873818-05: DOI: 10.1002/andp.201600270

Authors:Yichen Huang; Yong-Liang Zhang, Xie Chen Abstract: In many-body localized systems, propagation of information forms a light cone that grows logarithmically with time. However, local changes in energy or other conserved quantities typically spread only within a finite distance. Is it possible to detect the logarithmic light cone generated by a local perturbation from the response of a local operator at a later time' We numerically calculate various correlators in the random-field Heisenberg chain. While the equilibrium retarded correlator A(t=0)B(t>0) is not sensitive to the unbounded information propagation, the out-of-time-ordered correlator A(t=0)B(t>0)A(t=0)B(t>0) can detect the logarithmic light cone. We relate out-of-time-ordered correlators to the Lieb-Robinson bound in many-body localized systems, and show how to detect the logarithmic light cone with retarded correlators in specially designed states. Furthermore, we study the temperature dependence of the logarithmic light cone using out-of-time-ordered correlators.Recently, out-of-time-ordered correlators have been used extensively in quantum gravity to study chaos and scrambling of black holes via the AdS/CFT correspondence. This paper gives an example in which out-of-time-ordered correlators provide insights (beyond conventional correlators) into the dynamics of quantum many-body systems. In many-body localized systems, it is shown that out-of-time-ordered correlators can detect the logarithmic light cone (a characteristic feature of many-body localization), while equilibrium retarded correlators cannot. PubDate: 2016-12-09T14:27:02.471494-05: DOI: 10.1002/andp.201600318

Authors:Rahul Nandkishore; Sarang Gopalakrishnan Abstract: We consider what happens when a many body localized system is coupled to a heat bath. Unlike previous works, we do not restrict ourselves to the limit where the bath is large and effectively Markovian, nor to the limit where back action on the bath is negligible. We identify limits where the effect of the bath can be captured by classical noise, and limits where it cannot. We also identify limits in which the bath delocalizes the system, as well as limits in which the system localizes the bath. Using general arguments and dimensional analysis, we constrain the overall phase diagram of the coupled system and bath. Our analysis incorporates all the previously discussed regimes, and also uncovers a new intrinsically quantum regime that has not hitherto been discussed. We discuss baths that are themselves near a localization transition, or are strongly disordered but protected against localization by symmetry or topology. We also discuss situations where the system and bath have different dimensionality (the case of ‘boundary MBL’ and ‘boundary baths’).The paper examines the behavior of many body localized systems weakly coupled to heat baths either in the bulk or on the boundary. It identifies the key parameters, and elucidates the physics in each parameter regime. PubDate: 2016-11-25T04:50:57.307349-05: DOI: 10.1002/andp.201600181

Authors:Peter Nalbach; Samaneh Javanbakht, Christopher Stahl, Michael Thorwart Abstract: The two-state two-path model is introduced as a minimized model to describe the quantum dynamics of an electronic wave packet in the vicinity of a conical intersection. It involves two electronic potential energy surfaces each of which hosts a pair of quasi-classical trajectories over which the wave packet is assumed to be delocalized. When both trajectories evolve dynamically either diabatically or adiabatically, the full wave packet dynamics shows only features of the dynamics around avoided level crossings in the vicinity of the conical intersection. When one trajectory evolves adiabatically whereas the other trajectory follows a diabatic evolution, quantum mechanical interference of the wave packet components on each path generates Stueckelberg oscillations in the transition probability. These are surprisingly robust against a dissipative environment and, thus, should be a marker for conical intersections.The two-state two-path model is introduced as a minimal model to describe the quantum dynamics of an electronic wave packet in the vicinity of a conical intersection. The electron can be delocalized over a pair of quasi-classical trajectories living on two electronic potential surfaces. Non-trivial quantum interference of the wave packet components is found between the motion on the adiabatic and the diabatic paths, generating Stueckelberg oscillations. PubDate: 2016-10-27T01:30:39.399418-05: DOI: 10.1002/andp.201600147