
Reviews in Mathematical Physics [SJR: 1.092] [HI: 36] [0 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 0129055X  ISSN (Online) 17936659 Published by World Scientific [118 journals] 
 Bulkedge correspondence and the cobordism invariance of the index
 Authors: Shin Hayashi
Abstract: Reviews in Mathematical Physics, Volume 29, Issue 10, November 2017.
We show that the bulkedge correspondence for twodimensional type A and type [math] topological insulators follows directly from the cobordism invariance of the index.
Citation: Reviews in Mathematical Physics
PubDate: 20171107T02:44:10Z
DOI: 10.1142/S0129055X17500337
 Authors: Shin Hayashi
 On the algebraic quantization of a massive scalar field in antide Sitter
spacetime Authors: Claudio Dappiaggi, Hugo R. C. Ferreira
Abstract: Reviews in Mathematical Physics, Ahead of Print.
We discuss the algebraic quantization of a real, massive scalar field in the Poincaré patch of the [math]dimensional antide Sitter spacetime, with arbitrary boundary conditions. By using the functional formalism, we show that it is always possible to associate to such system an algebra of observables enjoying the standard properties of causality, timeslice axiom and Flocality. In addition, we characterize the wavefront set of the ground state associated to the system under investigation. As a consequence, we are able to generalize the definition of Hadamard states and construct a global algebra of Wick polynomials.
Citation: Reviews in Mathematical Physics
PubDate: 20171103T10:22:32Z
DOI: 10.1142/S0129055X18500046
 Authors: Claudio Dappiaggi, Hugo R. C. Ferreira
 Darboux transformations of integrable couplings and applications
 Authors: WenXiu Ma, YuJuan Zhang
Abstract: Reviews in Mathematical Physics, Ahead of Print.
A formulation of Darboux transformations is proposed for integrable couplings, based on nonsemisimple matrix Lie algebras. Applications to a kind of integrable couplings of the AKNS equations are made, along with an explicit formula for the associated Bäcklund transformation. Exact onesolitonlike solutions are computed for the integrable couplings of the second and thirdorder AKNS equations, and a type of reduction is created to generate integrable couplings and their onesolitonlike solutions for the NLS and MKdV equations.
Citation: Reviews in Mathematical Physics
PubDate: 20171030T07:40:24Z
DOI: 10.1142/S0129055X18500034
 Authors: WenXiu Ma, YuJuan Zhang
 3D flow of a compressible viscous micropolar fluid model with spherical
symmetry: A brief survey and recent progress Authors: Ivan Dražić
Abstract: Reviews in Mathematical Physics, Ahead of Print.
We consider the nonstationary 3D flow of a compressible viscous and heatconducting micropolar fluid with the assumption of spherical symmetry. We analyze the flow between two concentric spheres that present solid thermoinsulated walls. The fluid is perfect and polytropic in the thermodynamical sense and the initial density and temperature are strictly positive. The corresponding problem has homogeneous boundary data. In this work, we present the described model and provide a brief overview of the progress in the mathematical analysis of the associated initialboundary problem. We consider existence and uniqueness of the generalized solution, asymptotic behavior of the solution and regularity of the solution.
Citation: Reviews in Mathematical Physics
PubDate: 20171030T07:40:23Z
DOI: 10.1142/S0129055X18300017
 Authors: Ivan Dražić
 Infinite index extensions of local nets and defects
 Authors: Simone Del Vecchio, Luca Giorgetti
Abstract: Reviews in Mathematical Physics, Ahead of Print.
The subfactor theory provides a tool to analyze and construct extensions of Quantum Field Theories, once the latter are formulated as local nets of von Neumann algebras. We generalize some of the results of [62] to the case of extensions with infinite Jones index. This case naturally arises in physics, the canonical examples are given by global gauge theories with respect to a compact (nonfinite) group of internal symmetries. Building on the works of Izumi–Longo–Popa [44] and Fidaleo–Isola [30], we consider generalized Qsystems (of intertwiners) for a semidiscrete inclusion of properly infinite von Neumann algebras, which generalize ordinary Qsystems introduced by Longo [58] to the infinite index case. We characterize inclusions which admit generalized Qsystems of intertwiners and define a braided product among the latter, hence we construct examples of QFTs with defects (phase boundaries) of infinite index, extending the family of boundaries in the grasp of [7].
Citation: Reviews in Mathematical Physics
PubDate: 20171020T11:45:33Z
DOI: 10.1142/S0129055X18500022
 Authors: Simone Del Vecchio, Luca Giorgetti
 The 2Hilbert space of a prequantum bundle gerbe
 Authors: Severin Bunk, Christian Sämann, Richard J. Szabo
Abstract: Reviews in Mathematical Physics, Ahead of Print.
We construct a prequantum 2Hilbert space for any line bundle gerbe whose Dixmier–Douady class is torsion. Analogously to usual prequantization, this 2Hilbert space has the category of sections of the line bundle gerbe as its underlying 2vector space. These sections are obtained as certain morphism categories in Waldorf’s version of the 2category of line bundle gerbes. We show that these morphism categories carry a monoidal structure under which they are semisimple and abelian. We introduce a dual functor on the sections, which yields a closed structure on the morphisms between bundle gerbes and turns the category of sections into a 2Hilbert space. We discuss how these 2Hilbert spaces fit various expectations from higher prequantization. We then extend the transgression functor to the full 2category of bundle gerbes and demonstrate its compatibility with the additional structures introduced. We discuss various aspects of Kostant–Souriau prequantization in this setting, including its dimensional reduction to ordinary prequantization.
Citation: Reviews in Mathematical Physics
PubDate: 20171019T09:17:10Z
DOI: 10.1142/S0129055X18500010
 Authors: Severin Bunk, Christian Sämann, Richard J. Szabo
 On the classification of finite quasiquantum groups
 Authors: Mamta Balodi, HuaLin Huang, Shiv Datt Kumar
Abstract: Reviews in Mathematical Physics, Ahead of Print.
We give an overview of the classification results obtained so far for finite quasiquantum groups over an algebraically closed field of characteristic zero. The main classification results on basic quasiHopf algebras are obtained by Etingof, Gelaki, Nikshych, and Ostrik, and on dual quasiHopf algebras by Huang, Liu and Ye. The objective of this survey is to help in understanding the tools and methods used for the classification.
Citation: Reviews in Mathematical Physics
PubDate: 20171019T09:17:10Z
DOI: 10.1142/S0129055X17300035
 Authors: Mamta Balodi, HuaLin Huang, Shiv Datt Kumar
 Spectral representations of normal operators in quaternionic Hilbert
spaces via intertwining quaternionic PVMs Authors: Riccardo Ghiloni, Valter Moretti, Alessandro Perotti
Abstract: Reviews in Mathematical Physics, Ahead of Print.
The possibility of formulating quantum mechanics over quaternionic Hilbert spaces can be traced back to von Neumann’s foundational works in the thirties. The absence of a suitable quaternionic version of spectrum prevented the full development of the theory. The first rigorous quaternionic formulation has started only in 2007 with the definition of the spherical spectrum of a quaternionic operator based on a quadratic version of resolvent operator. The relevance of this notion is proved by the existence of a quaternionic continuous functional calculus and a theory of quaternionic semigroups relying upon it. A problem of the quaternionic formulation is the description of composite quantum systems in the absence of a natural tensor product due to noncommutativity of quaternions. A promising tool towards a solution is a quaternionic projectionvalued measure (PVM), making possible a tensor product of quaternionic operators with physical relevance. A notion with this property, called intertwining quaternionic PVM, is presented here. This foundational paper aims to investigate the interplay of this new mathematical object and the spherical spectral features of quaternionic generally unbounded normal operators. We discover, in particular, the existence of other spectral notions equivalent to the spherical ones, but based on a standard nonquadratic notion of resolvent operator.
Citation: Reviews in Mathematical Physics
PubDate: 20171019T09:17:09Z
DOI: 10.1142/S0129055X17500349
 Authors: Riccardo Ghiloni, Valter Moretti, Alessandro Perotti
 Scattering properties of two singularly interacting particles on the
halfline Authors: Sebastian Egger, Joachim Kerner
Abstract: Reviews in Mathematical Physics, Ahead of Print.
We analyze scattering in a system of two (distinguishable) particles moving on the halfline [math] under the influence of singular twoparticle interactions. Most importantly, due to the spatial localization of the interactions, the twobody problem is of a nonseparable nature. We will discuss the presence of embedded eigenvalues and using the obtained knowledge about the kernel of the resolvent, we prove a version of the limiting absorption principle. Furthermore, by an appropriate adaptation of the Lippmann–Schwinger approach, we are able to construct generalized eigenfunctions which consequently allow us to establish an explicit expression for the (onshell) scattering amplitude. An approximation of the scattering amplitude in the weakcoupling limit is also derived.
Citation: Reviews in Mathematical Physics
PubDate: 20170928T05:38:36Z
DOI: 10.1142/S0129055X17500325
 Authors: Sebastian Egger, Joachim Kerner
 Entangled spin chain
 Authors: Olof Salberger, Vladimir Korepin
Abstract: Reviews in Mathematical Physics, Ahead of Print.
We introduce a new model of interacting spin 1/2. It describes interactions of three nearest neighbors. The Hamiltonian can be expressed in terms of Fredkin gates. The Fredkin gate (also known as the controlled swap gate) is a computational circuit suitable for reversible computing. Our construction generalizes the model presented by Peter Shor and Ramis Movassagh to halfinteger spins. Our model can be solved by means of Catalan combinatorics in the form of random walks on the upper half plane of a square lattice (Dyck walks). Each Dyck path can be mapped on a wave function of spins. The ground state is an equally weighted superposition of Dyck walks (instead of Motzkin walks). We can also express it as a matrix product state. We further construct a model of interacting spins 3/2 and greater halfinteger spins. The models with higher spins require coloring of Dyck walks. We construct a [math] symmetric model (where [math] is the number of colors). The leading term of the entanglement entropy is then proportional to the square root of the length of the lattice (like in the Shor–Movassagh model). The gap closes as a high power of the length of the lattice [5, 11].
Citation: Reviews in Mathematical Physics
PubDate: 20170908T02:36:20Z
DOI: 10.1142/S0129055X17500313
 Authors: Olof Salberger, Vladimir Korepin
 On the dynamics of polarons in the strongcoupling limit
 Authors: Marcel Griesemer
Abstract: Reviews in Mathematical Physics, Ahead of Print.
The polaron model of H. Fröhlich describes an electron coupled to the quantized longitudinal optical modes of a polar crystal. In the strongcoupling limit, one expects that the phonon modes may be treated classically, which leads to a coupled Schrödinger–Poisson system with memory. For the effective dynamics of the electron, this amounts to a nonlinear and nonlocal Schrödinger equation. We use the Dirac–Frenkel variational principle to derive the Schrödinger–Poisson system from the Fröhlich model and we present new results on the accuracy of their solutions for describing the motion of Fröhlich polarons in the strongcoupling limit. Our main result extends to [math]polaron systems.
Citation: Reviews in Mathematical Physics
PubDate: 20170905T01:22:17Z
DOI: 10.1142/S0129055X17500301
 Authors: Marcel Griesemer
 Erratum: Full regularity for a C*algebra of the canonical commutation
relations Authors: Hendrik Grundling, KarlHermann Neeb
Abstract: Reviews in Mathematical Physics, Ahead of Print.
The proof of the main theorem of the paper [1] contains an error. We are grateful to Professor Ralf Meyer (Mathematisches Institut, GeorgAugust Universität Göttingen) for pointing out this mistake.
Citation: Reviews in Mathematical Physics
PubDate: 20170829T06:27:34Z
DOI: 10.1142/S0129055X17920027
 Authors: Hendrik Grundling, KarlHermann Neeb