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PHYSICS (585 journals)

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Journal Cover Reviews in Mathematical Physics
  [SJR: 1.092]   [H-I: 36]   [0 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0129-055X - ISSN (Online) 1793-6659
   Published by World Scientific Homepage  [117 journals]
  • Bulk-edge 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 bulk-edge correspondence for two-dimensional type A and type [math] topological insulators follows directly from the cobordism invariance of the index.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-11-07T02:44:10Z
      DOI: 10.1142/S0129055X17500337
  • On the algebraic quantization of a massive scalar field in anti-de Sitter
    • 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 anti-de 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, time-slice axiom and F-locality. 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: 2017-11-03T10:22:32Z
      DOI: 10.1142/S0129055X18500046
  • Darboux transformations of integrable couplings and applications
    • Authors: Wen-Xiu Ma, Yu-Juan Zhang
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      A formulation of Darboux transformations is proposed for integrable couplings, based on non-semisimple 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 one-soliton-like solutions are computed for the integrable couplings of the second- and third-order AKNS equations, and a type of reduction is created to generate integrable couplings and their one-soliton-like solutions for the NLS and MKdV equations.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-10-30T07:40:24Z
      DOI: 10.1142/S0129055X18500034
  • 3-D 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 non-stationary 3-D flow of a compressible viscous and heat-conducting micropolar fluid with the assumption of spherical symmetry. We analyze the flow between two concentric spheres that present solid thermo-insulated 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 initial-boundary 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: 2017-10-30T07:40:23Z
      DOI: 10.1142/S0129055X18300017
  • 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 (non-finite) group of internal symmetries. Building on the works of Izumi–Longo–Popa [44] and Fidaleo–Isola [30], we consider generalized Q-systems (of intertwiners) for a semidiscrete inclusion of properly infinite von Neumann algebras, which generalize ordinary Q-systems introduced by Longo [58] to the infinite index case. We characterize inclusions which admit generalized Q-systems 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: 2017-10-20T11:45:33Z
      DOI: 10.1142/S0129055X18500022
  • The 2-Hilbert 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 2-Hilbert space for any line bundle gerbe whose Dixmier–Douady class is torsion. Analogously to usual prequantization, this 2-Hilbert space has the category of sections of the line bundle gerbe as its underlying 2-vector space. These sections are obtained as certain morphism categories in Waldorf’s version of the 2-category 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 2-Hilbert space. We discuss how these 2-Hilbert spaces fit various expectations from higher prequantization. We then extend the transgression functor to the full 2-category 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: 2017-10-19T09:17:10Z
      DOI: 10.1142/S0129055X18500010
  • On the classification of finite quasi-quantum groups
    • Authors: Mamta Balodi, Hua-Lin 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 quasi-quantum groups over an algebraically closed field of characteristic zero. The main classification results on basic quasi-Hopf algebras are obtained by Etingof, Gelaki, Nikshych, and Ostrik, and on dual quasi-Hopf 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: 2017-10-19T09:17:10Z
      DOI: 10.1142/S0129055X17300035
  • 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 non-commutativity of quaternions. A promising tool towards a solution is a quaternionic projection-valued 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 non-quadratic notion of resolvent operator.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-10-19T09:17:09Z
      DOI: 10.1142/S0129055X17500349
  • Scattering properties of two singularly interacting particles on the
    • 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 half-line [math] under the influence of singular two-particle interactions. Most importantly, due to the spatial localization of the interactions, the two-body problem is of a non-separable 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 (on-shell) scattering amplitude. An approximation of the scattering amplitude in the weak-coupling limit is also derived.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-09-28T05:38:36Z
      DOI: 10.1142/S0129055X17500325
  • 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 half-integer 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 half-integer 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: 2017-09-08T02:36:20Z
      DOI: 10.1142/S0129055X17500313
  • On the dynamics of polarons in the strong-coupling 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 strong-coupling 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 non-local 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 strong-coupling limit. Our main result extends to [math]-polaron systems.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-09-05T01:22:17Z
      DOI: 10.1142/S0129055X17500301
  • Erratum: Full regularity for a C*-algebra of the canonical commutation
    • Authors: Hendrik Grundling, Karl-Hermann 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, Georg-August Universität Göttingen) for pointing out this mistake.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-08-29T06:27:34Z
      DOI: 10.1142/S0129055X17920027
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