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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  [118 journals]
  • Loop groups and noncommutative geometry
    • Authors: Sebastiano Carpi, Robin Hillier
      Abstract: Reviews in Mathematical Physics, Volume 29, Issue 09, October 2017.
      We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level [math] projective unitary positive-energy representations of any given loop group [math]. The construction is based on certain supersymmetric conformal field theory models associated with [math] in the setting of conformal nets. We then generalize the construction to many other rational chiral conformal field theory models including coset models and the moonshine conformal net.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-09-07T07:38:40Z
      DOI: 10.1142/S0129055X17500295
  • 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
  • Theoretical investigations of an information geometric approach to
    • Authors: Sean Alan Ali, Carlo Cafaro
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. The existence of fundamental links among physical systems, dynamical equations, experimental data and statistical modeling motivate us to present in this paper our theoretical modeling scheme which combines information geometry and inductive inference methods to provide a probabilistic description of complex systems in the presence of limited information. Special focus is devoted to describe the role of our entropic information geometric complexity measure. In particular, we provide several illustrative examples wherein our modeling scheme is used to infer macroscopic predictions when only partial knowledge of the microscopic nature of a given system is available. Finally, limitations, possible improvements, and future investigations are discussed.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-08-17T06:27:46Z
      DOI: 10.1142/S0129055X17300023
  • A compositional framework for reaction networks
    • Authors: John C. Baez, Blake S. Pollard
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      Reaction networks, or equivalently Petri nets, are a general framework for describing processes in which entities of various kinds interact and turn into other entities. In chemistry, where the reactions are assigned ‘rate constants’, any reaction network gives rise to a nonlinear dynamical system called its ‘rate equation’. Here we generalize these ideas to ‘open’ reaction networks, which allow entities to flow in and out at certain designated inputs and outputs. We treat open reaction networks as morphisms in a category. Composing two such morphisms connects the outputs of the first to the inputs of the second. We construct a functor sending any open reaction network to its corresponding ‘open dynamical system’. This provides a compositional framework for studying the dynamics of reaction networks. We then turn to statics: that is, steady state solutions of open dynamical systems. We construct a ‘black-boxing’ functor that sends any open dynamical system to the relation that it imposes between input and output variables in steady states. This extends our earlier work on black-boxing for Markov processes.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-07-31T05:44:59Z
      DOI: 10.1142/S0129055X17500283
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