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MATHEMATICS (643 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 6)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 20)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 10)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 4)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 15)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 3)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 9)
Algorithms Research     Open Access  
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Numerical Analysis & Computational Mathematics     Hybrid Journal   (Followers: 5)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 17)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 1)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 5)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 1)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 4)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)

        1 2 3 4 | Last

Journal Cover Communications in Mathematical Physics
  [SJR: 1.76]   [H-I: 101]   [1 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1432-0916 - ISSN (Online) 0010-3616
   Published by Springer-Verlag Homepage  [2335 journals]
  • Multivariate Trace Inequalities
    • Authors: David Sutter; Mario Berta; Marco Tomamichel
      Pages: 37 - 58
      Abstract: Abstract We prove several trace inequalities that extend the Golden–Thompson and the Araki–Lieb–Thirring inequality to arbitrarily many matrices. In particular, we strengthen Lieb’s triple matrix inequality. As an example application of our four matrix extension of the Golden–Thompson inequality, we prove remainder terms for the monotonicity of the quantum relative entropy and strong sub-additivity of the von Neumann entropy in terms of recoverability. We find the first explicit remainder terms that are tight in the commutative case. Our proofs rely on complex interpolation theory as well as asymptotic spectral pinching, providing a transparent approach to treat generic multivariate trace inequalities.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2778-5
      Issue No: Vol. 352, No. 1 (2017)
  • Universal Preparability of States and Asymptotic Completeness
    • Authors: Rolf Gohm; Florian Haag; Burkhard Kümmerer
      Pages: 59 - 94
      Abstract: Abstract We introduce a notion of universal preparability for a state of a system, more precisely: for a normal state on a von Neumann algebra. It describes a situation where from an arbitrary initial state it is possible to prepare a target state with arbitrary precision by a repeated interaction with a sequence of copies of another system. For \({\mathcal{B}(\mathcal{H})}\) we give criteria sufficient to ensure that all normal states are universally preparable which can be verified for a class of non-commutative birth and death processes realized, in particular, by the interaction of a micromaser with a stream of atoms. As a tool, the theory of tight sequences of states and of stationary states is further developed and we show that in the presence of stationary faithful normal states universal preparability of all normal states is equivalent to asymptotic completeness, a notion studied earlier in connection with the scattering theory of non-commutative Markov processes.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-017-2851-8
      Issue No: Vol. 352, No. 1 (2017)
  • Planar Para Algebras, Reflection Positivity
    • Authors: Arthur Jaffe; Zhengwei Liu
      Pages: 95 - 133
      Abstract: Abstract We define a planar para algebra, which arises naturally from combining planar algebras with the idea of \({\mathbb{Z}_{N}}\) para symmetry in physics. A subfactor planar para algebra is a Hilbert space representation of planar tangles with parafermionic defects that are invariant under para isotopy. For each \({\mathbb{Z}_{N}}\) , we construct a family of subfactor planar para algebras that play the role of Temperley–Lieb–Jones planar algebras. The first example in this family is the parafermion planar para algebra (PAPPA). Based on this example, we introduce parafermion Pauli matrices, quaternion relations, and braided relations for parafermion algebras, which one can use in the study of quantum information. An important ingredient in planar para algebra theory is the string Fourier transform (SFT), which we use on the matrix algebra generated by the Pauli matrices. Two different reflections play an important role in the theory of planar para algebras. One is the adjoint operator; the other is the modular conjugation in Tomita–Takesaki theory. We use the latter one to define the double algebra and to introduce reflection positivity. We give a new and geometric proof of reflection positivity by relating the two reflections through the string Fourier transform.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2779-4
      Issue No: Vol. 352, No. 1 (2017)
  • Quantum Sheaf Cohomology on Grassmannians
    • Authors: Jirui Guo; Zhentao Lu; Eric Sharpe
      Pages: 135 - 184
      Abstract: Abstract In this paper we study the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle. Quantum sheaf cohomology is a (0,2) deformation of the ordinary quantum cohomology ring, realized as the OPE ring in A/2-twisted theories. Quantum sheaf cohomology has previously been computed for abelian gauged linear sigma models (GLSMs); here, we study (0,2) deformations of nonabelian GLSMs, for which previous methods have been intractable. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. We also utilize recent advances in supersymmetric localization to compute A/2 correlation functions and check the general result in examples. In this paper we focus on physics derivations and examples; in a companion paper, we will provide a mathematically rigorous derivation of the classical sheaf cohomology ring.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2763-z
      Issue No: Vol. 352, No. 1 (2017)
  • The Spinning Particle with Curved Target
    • Authors: Ezra Getzler
      Pages: 185 - 199
      Abstract: Abstract We extend our previous calculation of the BV cohomology of the spinning particle with a flat target to the general case, in which the target carries a non-trivial pseudo-Riemannian metric and a magnetic field.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2764-y
      Issue No: Vol. 352, No. 1 (2017)
  • On the Asymptotic Stability of Steady Flows with Nonzero Flux in
           Two-Dimensional Exterior Domains
    • Authors: Julien Guillod
      Pages: 201 - 214
      Abstract: Abstract The Navier–Stokes equations in a two-dimensional exterior domain are considered. The asymptotic stability of stationary solutions satisfying a general hypothesis is proven under any L 2-perturbation. In particular, the general hypothesis is valid if the steady solution is the sum of the critically decaying flux carrier with flux \({\left \Phi \right < 2 \pi}\) and a small subcritically decaying term. Under the central symmetry assumption, the general hypothesis is also proven for any critically decaying steady solutions under a suitable smallness condition.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2794-5
      Issue No: Vol. 352, No. 1 (2017)
  • Dynamics Near the Ground State for the Energy Critical Nonlinear Heat
           Equation in Large Dimensions
    • Authors: Charles Collot; Frank Merle; Pierre Raphaël
      Pages: 215 - 285
      Abstract: Abstract We consider the energy critical semilinear heat equation $$\partial_tu = \Delta u + u ^{\frac{4}{d-2}}u, \quad x \in \mathbb{R}^d$$ and give a complete classification of the flow near the ground state solitary wave $$Q(x) = \frac{1}{\left(1+\frac{ x ^2}{d(d-2)}\right)^{\frac{d-2}{2}}}$$ in dimension \({d \ge 7}\) , in the energy critical topology and without radial symmetry assumption. Given an initial data \({Q + \varepsilon_0}\) with \({\ \nabla \varepsilon_0\ _{L^2} \ll 1}\) , the solution either blows up in the ODE type I regime, or dissipates, and these two open sets are separated by a codimension one set of solutions asymptotically attracted by the solitary wave. In particular, non self similar type II blow up is ruled out in dimension \({d \ge 7}\) near the solitary wave even though it is known to occur in smaller dimensions (Schweyer, J Funct Anal 263(12):3922–3983, 2012). Our proof is based on sole energy estimates deeply connected to Martel et al. (Acta Math 212(1):59–140, 2014) and draws a route map for the classification of the flow near the solitary wave in the energy critical setting. A by-product of our method is the classification of minimal elements around Q belonging to the unstable manifold.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2795-4
      Issue No: Vol. 352, No. 1 (2017)
  • Noncommutative Principal Bundles Through Twist Deformation
    • Authors: Paolo Aschieri; Pierre Bieliavsky; Chiara Pagani; Alexander Schenkel
      Pages: 287 - 344
      Abstract: Abstract We construct noncommutative principal bundles deforming principal bundles with a Drinfeld twist (2-cocycle). If the twist is associated with the structure group then we have a deformation of the fibers. If the twist is associated with the automorphism group of the principal bundle, then we obtain noncommutative deformations of the base space as well. Combining the two twist deformations we obtain noncommutative principal bundles with both noncommutative fibers and base space. More in general, the natural isomorphisms proving the equivalence of a closed monoidal category of modules and its twist related one are used to obtain new Hopf–Galois extensions as twists of Hopf–Galois extensions. A sheaf approach is also considered, and examples presented.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2765-x
      Issue No: Vol. 352, No. 1 (2017)
  • Non-topological Vortex Configurations in the ABJM Model
    • Authors: Xiaosen Han; Gabriella Tarantello
      Pages: 345 - 385
      Abstract: Abstract In this paper we study the existence of vortex-type solutions for a system of self-dual equations deduced from the mass-deformed Aharony–Bergman–Jafferis–Maldacena (ABJM) model. The governing equations, derived by Mohammed, Murugan, and Nastse under suitable ansatz involving fuzzy sphere matrices, have the new feature that they can support only non-topological vortex solutions. After transforming the self-dual equations into a nonlinear elliptic \({2\times 2}\) system we prove first an existence result by means of a perturbation argument based on a new and appropriate scaling for the solutions. Subsequently, we prove a more complete existence result by using a dynamical analysis together with a blow-up argument. In this way we establish that any positive energy level is attained by a 1-parameter family of vortex solutions, which also correspond to (constraint) energy minimizers. In other words, we register the exceptional fact in a BPS-setting that, neither a “quantization” effect nor an energy gap is induced upon the system by the rigid “critical” coupling of the self-dual regime.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2817-2
      Issue No: Vol. 352, No. 1 (2017)
  • Negative Energy Ground States for the L 2 -Critical NLSE on Metric Graphs
    • Authors: Riccardo Adami; Enrico Serra; Paolo Tilli
      Pages: 387 - 406
      Abstract: Abstract We investigate the existence of ground states with prescribed mass for the focusing nonlinear Schrödinger equation with L 2-critical power nonlinearity on noncompact quantum graphs. We prove that, unlike the case of the real line, for certain classes of graphs there exist ground states with negative energy for a whole interval of masses. A key role is played by a thorough analysis of Gagliardo–Nirenberg inequalities and by estimates of the optimal constants. Most of the techniques are new and suited to the investigation of variational problems on metric graphs.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2797-2
      Issue No: Vol. 352, No. 1 (2017)
  • Bit Threads and Holographic Entanglement
    • Authors: Michael Freedman; Matthew Headrick
      Pages: 407 - 438
      Abstract: Abstract The Ryu-Takayanagi (RT) formula relates the entanglement entropy of a region in a holographic theory to the area of a corresponding bulk minimal surface. Using the max flow-min cut principle, a theorem from network theory, we rewrite the RT formula in a way that does not make reference to the minimal surface. Instead, we invoke the notion of a “flow”, defined as a divergenceless norm-bounded vector field, or equivalently a set of Planck-thickness “bit threads”. The entanglement entropy of a boundary region is given by the maximum flux out of it of any flow, or equivalently the maximum number of bit threads that can emanate from it. The threads thus represent entanglement between points on the boundary, and naturally implement the holographic principle. As we explain, this new picture clarifies several conceptual puzzles surrounding the RT formula. We give flow-based proofs of strong subadditivity and related properties; unlike the ones based on minimal surfaces, these proofs correspond in a transparent manner to the properties’ information-theoretic meanings. We also briefly discuss certain technical advantages that the flows offer over minimal surfaces. In a mathematical appendix, we review the max flow-min cut theorem on networks and on Riemannian manifolds, and prove in the network case that the set of max flows varies Lipshitz continuously in the network parameters.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2796-3
      Issue No: Vol. 352, No. 1 (2017)
  • Ballistic Transport and Absolute Continuity of One-Frequency
           Schrödinger Operators
    • Authors: Zhiyuan Zhang; Zhiyan Zhao
      Pages: 877 - 921
      Abstract: Abstract For the solution u(t) to the discrete Schrödinger equation $$ {\rm i} \frac{d}{dt}u_n(t)=-(u_{n+1}(t)+u_{n-1}(t))+V(\theta + n\alpha)u_n(t), \quad n\in\mathbb{Z},$$ with \({\alpha\in\mathbb{R}{\setminus} \mathbb{Q}}\) and \({V\in C^\omega(\mathbb{T},\mathbb{R})}\) , we consider the growth rate with t of its diffusion norm \({\langle u(t)\rangle_{p}:=\left(\sum_{n\in\mathbb{Z}}(n^{p}+1) u_n(t) ^2\right)^\frac12}\) , and the (non-averaged) transport exponents $$\beta_u^{+}(p) := \limsup_{t \to \infty} \frac{2\log \langle u(t)\rangle_{p}}{p\log t}, \quad \beta_u^{-}(p):= \liminf_{t \to \infty} \frac{2\log \langle u(t)\rangle_{p}}{p\log t}.$$ We will show that, if the corresponding Schrödinger operator has purely absolutely continuous spectrum, then \({\beta_{u}^{\pm}(p)=1}\) , provided that u(0) is well localized.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-017-2848-3
      Issue No: Vol. 351, No. 3 (2017)
  • Singular Behavior of the Leading Lyapunov Exponent of a Product of Random
           $${2 \times 2}$$ 2 × 2 Matrices
    • Authors: Giuseppe Genovese; Giambattista Giacomin; Rafael Leon Greenblatt
      Pages: 923 - 958
      Abstract: Abstract We consider a certain infinite product of random \({2 \times 2}\) matrices appearing in the solution of some 1 and 1 + 1 dimensional disordered models in statistical mechanics, which depends on a parameter \({\varepsilon > 0}\) and on a real random variable with distribution \({\mu}\) . For a large class of \({\mu}\) , we prove the prediction by Derrida and Hilhorst (J Phys A 16:2641, 1983) that the Lyapunov exponent behaves like \({C \epsilon^{2 \alpha}}\) in the limit \({\epsilon \searrow 0}\) , where \({\alpha \in (0,1)}\) and \({C > 0}\) are determined by \({\mu}\) . Derrida and Hilhorst performed a two-scale analysis of the integral equation for the invariant distribution of the Markov chain associated to the matrix product and obtained a probability measure that is expected to be close to the invariant one for small \({\epsilon}\) . We introduce suitable norms and exploit contractivity properties to show that such a probability measure is indeed close to the invariant one in a sense that implies a suitable control of the Lyapunov exponent.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-017-2855-4
      Issue No: Vol. 351, No. 3 (2017)
  • Mode Stability of Self-Similar Wave Maps in Higher Dimensions
    • Authors: Ovidiu Costin; Roland Donninger; Irfan Glogić
      Pages: 959 - 972
      Abstract: Abstract We consider co-rotational wave maps from Minkowski space in d + 1 dimensions to the d-sphere. Recently, Bizoń and Biernat found explicit self-similar solutions for each dimension \({d\geq 4}\) . We give a rigorous proof for the mode stability of these self-similar wave maps.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2776-7
      Issue No: Vol. 351, No. 3 (2017)
  • Universal Positive Mass Theorems
    • Authors: Marc Herzlich
      Pages: 973 - 992
      Abstract: Abstract In this paper, we develop a general study of contributions at infinity of Bochner–Weitzenböck-type formulas on asymptotically flat manifolds, inspired by Witten’s proof of the positive mass theorem. As an application, we show that similar proofs can be obtained in a much more general setting as any choice of an irreducible natural bundle and a very large choice of first-order operators may lead to a positive mass theorem along the same lines if the necessary curvature conditions are satisfied.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2777-6
      Issue No: Vol. 351, No. 3 (2017)
  • Integrable Magnetic Geodesic Flows on 2-Torus: New Examples via
           Quasi-Linear System of PDEs
    • Authors: S. V. Agapov; M. Bialy; A. E. Mironov
      Pages: 993 - 1007
      Abstract: Abstract For a magnetic geodesic flow on the 2-torus the only known integrable example is that of a flow integrable for all energy levels. It has an integral linear in momenta and corresponds to a one parameter group preserving the Lagrangian function of the magnetic flow. In this paper the problem of integrability on a single energy level is considered. Then, in addition to the example mentioned above, a few other explicit examples with quadratic in momenta integrals can be constructed by means of the Maupertuis’ principle. Recently we proved that such an integrability problem can be reduced to a remarkable semi-Hamiltonian system of quasi-linear PDEs and to the question of the existence of smooth periodic solutions for this system. Our main result of the present paper states that any Liouville metric with the zero magnetic field on the 2-torus can be analytically deformed to a Riemannian metric with a small magnetic field so that the magnetic geodesic flow on an energy level is integrable by means of an integral quadratic in momenta.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2822-5
      Issue No: Vol. 351, No. 3 (2017)
  • Monoidal Supercategories
    • Authors: Jonathan Brundan; Alexander P. Ellis
      Pages: 1045 - 1089
      Abstract: Abstract This work is a companion to our article “Super Kac–Moody 2-categories,” which introduces super analogs of the Kac–Moody 2-categories of Khovanov–Lauda and Rouquier. In the case of \({\mathfrak{sl}_2}\) , the super Kac–Moody 2-category was constructed already in [A. Ellis and A. Lauda, “An odd categorification of \({U_q(\mathfrak{sl}_2)}\) ”], but we found that the formalism adopted there became too cumbersome in the general case. Instead, it is better to work with 2-supercategories (roughly, 2-categories enriched in vector superspaces). Then the Ellis–Lauda 2-category, which we call here a \({\Pi}\) -2-category (roughly, a 2-category equipped with a distinguished involution in its Drinfeld center), can be recovered by taking the superadditive envelope then passing to the underlying 2-category. The main goal of this article is to develop this language and the related formal constructions in the hope that these foundations may prove useful in other contexts.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-017-2850-9
      Issue No: Vol. 351, No. 3 (2017)
  • Singular Continuous Spectrum for Singular Potentials
    • Authors: Svetlana Jitomirskaya; Fan Yang
      Pages: 1127 - 1135
      Abstract: Abstract We prove that Schrödinger operators with meromorphic potentials \({(H_{\alpha,\theta}u)_n=u_{n+1}+u_{n-1}+ \frac{g(\theta+n\alpha)}{f(\theta+n\alpha)} u_n}\) have purely singular continuous spectrum on the set \({\{E: L(E) < \delta{(\alpha, \theta)}\}}\) , where \({\delta}\) is an explicit function and L is the Lyapunov exponent. This extends results of Jitomirskaya and Liu (Arithmetic spectral transitions for the Maryland model. CPAM, to appear) for the Maryland model and of Avila,You and Zhou (Sharp Phase transitions for the almost Mathieu operator. Preprint, 2015) for the almost Mathieu operator to the general family of meromorphic potentials.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2823-4
      Issue No: Vol. 351, No. 3 (2017)
  • Comparison of Unitary Duals of Drinfeld Doubles and Complex Semisimple Lie
    • Authors: Yuki Arano
      Pages: 1137 - 1147
      Abstract: Abstract We determine a substantial part of the unitary representation theory of the Drinfeld double of a q-deformation of a compact Lie group in terms of the complexification of the compact Lie group. Using this, we show that the dual of every q-deformation of a higher rank compact Lie group has central property (T). We also determine the unitary dual of \({SL_q(n,\mathbb{C})}\) .
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2704-x
      Issue No: Vol. 351, No. 3 (2017)
  • Non-Perturbative Localization with Quasiperiodic Potential in Continuous
    • Authors: Ilia Binder; Damir Kinzebulatov; Mircea Voda
      Pages: 1149 - 1175
      Abstract: Abstract We consider continuous one-dimensional multifrequency Schrödinger operators, with analytic potential, and prove Anderson localization in the regime of positive Lyapunov exponent for almost all phases and almost all Diophantine frequencies.
      PubDate: 2017-05-01
      DOI: 10.1007/s00220-016-2723-7
      Issue No: Vol. 351, No. 3 (2017)
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Edinburgh, EH14 4AS, UK
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