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  • New realizations of algebras of the Askey–Wilson type in terms of Lie and quantum algebras
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-07-20
    Nicolas Crampé; Dounia Shaaban Kabakibo; Luc Vinet

    The Askey–Wilson algebra is realized in terms of the elements of the quantum algebras Uq(𝔰𝔲(2)) or Uq(𝔰𝔲(1,1)). A new realization of the Racah algebra in terms of the Lie algebras 𝔰𝔲(2) or 𝔰𝔲(1,1) is also given. Details for different specializations are provided. The advantage of these new realizations is that one generator of the Askey–Wilson (or Racah) algebra becomes diagonal in the usual

    更新日期:2020-08-05
  • Thin domain limit and counterexamples to strong diamagnetism
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-08-05
    Bernard Helffer; Ayman Kachmar

    We study the magnetic Laplacian and the Ginzburg–Landau functional in a thin planar, smooth, tubular domain and with a uniform applied magnetic field. We provide counterexamples to strong diamagnetism, and as a consequence, we prove that the transition from the superconducting to the normal state is non-monotone. In some nonlinear regime, we determine the structure of the order parameter and compute

    更新日期:2020-08-04
  • On the absence of stationary currents
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-07-27
    Sven Bachmann; Martin Fraas

    We review the proofs of a theorem of Bloch on the absence of macroscopic stationary currents in quantum systems. The standard proof shows that the current in 1D vanishes in the large volume limit under rather general conditions. In higher dimensions, the total current across a cross-section does not need to vanish in gapless systems but it does vanish in gapped systems. We focus on the latter claim

    更新日期:2020-07-27
  • Boltzmann–Grad asymptotic behavior of collisional dynamics
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-07-03
    V. I. Gerasimenko; I. V. Gapyak

    This paper discusses some of the latest advances in the mathematical understanding of the nature of kinetic equations that describe the collective behavior of many-particle systems with collisional dynamics.

    更新日期:2020-07-24
  • Entropy driven transformations of statistical hypersurfaces
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-07-03
    Mario Angelelli; Boris Konopelchenko

    Deformations of geometric characteristics of statistical hypersurfaces governed by the law of growth of entropy are studied. Both general and special cases of deformations are considered. The basic structure of the statistical hypersurface is explored through a differential relation for the variables, and connections with the replicator dynamics for Gibbs’ weights are highlighted. Ideal and super-ideal

    更新日期:2020-07-24
  • Spectral asymptotics on stationary space-times
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-05-28
    Alexander Strohmaier; Steve Zelditch

    We review our recent relativistic generalization of the Gutzwiller–Duistermaat–Guillemin trace formula and Weyl law on globally hyperbolic stationary space-times with compact Cauchy hypersurfaces. We also discuss anticipated generalizations to non-compact Cauchy hypersurface cases.

    更新日期:2020-07-24
  • Bosonic collective excitations in Fermi gases
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-05-22
    Niels Benedikter

    Hartree–Fock theory has been justified as a mean-field approximation for fermionic systems. However, it suffers from some defects in predicting physical properties, making necessary a theory of quantum correlations. Recently, bosonization of many-body correlations has been rigorously justified as an upper bound on the correlation energy at high density with weak interactions. We review the bosonic

    更新日期:2020-07-24
  • Scattering of particles bounded to an infinite planar curve
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-05-12
    J. Dittrich

    Non-relativistic quantum particles bounded to a curve in ℝ2 by attractive contact δ-interaction are considered. The interval between the energy of the transversal bound state and zero is shown to belong to the absolutely continuous spectrum, with possible embedded eigenvalues. The existence of the wave operators is proved for the mentioned energy interval using the Hamiltonians with the interaction

    更新日期:2020-05-12
  • On the Koszul formula in noncommutative geometry
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-05-12
    Jyotishman Bhowmick; Debashish Goswami; Giovanni Landi

    We prove a Koszul formula for the Levi-Civita connection for any pseudo-Riemannian bilinear metric on a class of centered bimodule of noncommutative one-forms. As an application to the Koszul formula, we show that our Levi-Civita connection is a bimodule connection. We construct a spectral triple on a fuzzy sphere and compute the scalar curvature for the Levi-Civita connection associated to a canonical

    更新日期:2020-05-12
  • Canonical quantization of constants of motion
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-05-06
    Fabián Belmonte

    We develop a quantization method, that we name decomposable Weyl quantization, which ensures that the constants of motion of a prescribed finite set of Hamiltonians are preserved by the quantization. Our method is based on a structural analogy between the notions of reduction of the classical phase space and diagonalization of selfadjoint operators. We obtain the spectral decomposition of the emerging

    更新日期:2020-05-06
  • Random Schrödinger operators and Anderson localization in aperiodic media
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-05-06
    C. Rojas-Molina

    In this note, we review some results on localization and related properties for random Schrödinger operators arising in aperiodic media. These include the Anderson model associated to disordered quasicrystals and also the so-called Delone operators, operators associated to deterministic aperiodic structures.

    更新日期:2020-05-06
  • Strict deformation quantization of the state space of Mk(ℂ) with applications to the Curie–Weiss model
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-04-29
    Klaas Landsman; Valter Moretti; Christiaan J. F. van de Ven

    Increasing tensor powers of the k×k matrices Mk(ℂ) are known to give rise to a continuous bundle of C∗-algebras over I={0}∪1/ℕ⊂[0,1] with fibers A1/N=Mk(ℂ)⊗N and A0=C(Xk), where Xk=S(Mk(ℂ)), the state space of Mk(ℂ), which is canonically a compact Poisson manifold (with stratified boundary). Our first result is the existence of a strict deformation quantization of Xk à la Rieffel, defined by perfectly

    更新日期:2020-04-29
  • Dynamics of two qubits in common environment
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-04-28
    E. Bratus; L. Pastur

    We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment. We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso- and even nanosize. We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment

    更新日期:2020-04-28
  • Topological recursion and geometry
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-04-22
    Gaëtan Borot

    This paper aims at explaining some incarnations of the idea of topological recursion: in two-dimensional quantum field theories (2d TQFTs), in cohomological field theories (CohFT), and in the computation of volumes of the moduli space of curves. It gives an introduction to the formalism of quantum Airy structures on which the topological recursion is based, which is seen at work in the above topics

    更新日期:2020-04-22
  • On the regularity of Cauchy hypersurfaces and temporal functions in closed cone structures
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-04-22
    Ettore Minguzzi

    We complement our work on the causality of upper semi-continuous distributions of cones with some results on Cauchy hypersurfaces. We prove that every locally stably acausal Cauchy hypersurface is stable. Then we prove that the signed distance dS from a spacelike hypersurface S is, in a neighborhood of it, as regular as the hypersurface, and by using this fact we give a proof that every Cauchy hypersurface

    更新日期:2020-04-22
  • Ring chains with vertex coupling of a preferred orientation
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-04-16
    Marzieh Baradaran; Pavel Exner; Miloš Tater

    We consider a family of Schrödinger operators supported by a periodic chain of loops connected either tightly or loosely through connecting links of the length ℓ>0 with the vertex coupling which is non-invariant with respect to the time reversal. The spectral behavior of the model illustrates that the high-energy behavior of such vertices is determined by the vertex parity. The positive spectrum of

    更新日期:2020-04-16
  • Introduction to the BV-BFV formalism
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-04-14
    Alberto S. Cattaneo; Nima Moshayedi

    These notes give an introduction to the mathematical framework of the Batalin–Vilkovisky and Batalin–Fradkin–Vilkovisky formalisms.

    更新日期:2020-04-14
  • The excitation spectrum of the Bose gas in the Gross–Pitaevskii regime
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-04-09
    Chiara Boccato

    We consider a gas of interacting bosons trapped in a box of side length one in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s prediction for the ground state energy and the low-energy excitation spectrum. This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.

    更新日期:2020-04-09
  • K-theory of AF-algebras from braided C*-tensor categories
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-03-25
    Andreas Næs Aaserud; David Emrys Evans

    Renault, Wassermann, Handelman and Rossmann (early 1980s) and Evans and Gould (1994) explicitly described the K-theory of certain unital AF-algebras A as (quotients of) polynomial rings. In this paper, we show that in each case the multiplication in the polynomial ring (quotient) is induced by a ∗-homomorphism A⊗A→A arising from a unitary braiding on a C*-tensor category and essentially defined by

    更新日期:2020-03-25
  • Spectral measures for G2, II: Finite subgroups
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-03-23
    David E. Evans; Mathew Pugh

    Joint spectral measures associated to the rank two Lie group G2, including the representation graphs for the irreducible representations of G2 and its maximal torus, nimrep graphs associated to the G2 modular invariants have been studied. In this paper, we study the joint spectral measures for the McKay graphs (or representation graphs) of finite subgroups of G2. Using character theoretic methods we

    更新日期:2020-03-23
  • On ℤ2-indices for ground states of fermionic chains
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-03-16
    Chris Bourne; Hermann Schulz-Baldes

    For parity-conserving fermionic chains, we review how to associate ℤ2-indices to ground states in finite systems with quadratic and higher-order interactions as well as to quasifree ground states on the infinite CAR algebra. It is shown that the ℤ2-valued spectral flow provides a topological obstruction for two systems to have the same ℤ2-index. A rudimentary definition of a ℤ2-phase label for a class

    更新日期:2020-03-16
  • Středa formula for charge and spin currents
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-03-11
    Domenico Monaco; Massimo Moscolari

    We consider a 2-dimensional Bloch–Landau–Pauli Hamiltonian for a spinful electron in a constant magnetic field subject to a periodic background potential. Assuming that the z-component of the spin operator is conserved, we compute the linear response of the associated spin density of states to a small change in the magnetic field, and identify it with the spin Hall conductivity. This response is in

    更新日期:2020-03-11
  • Classification of first order sesquilinear forms
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-03-05
    Matteo Capoferri; Nikolai Saveliev; Dmitri Vassiliev

    A natural way to obtain a system of partial differential equations on a manifold is to vary a suitably defined sesquilinear form. The sesquilinear forms we study are Hermitian forms acting on sections of the trivial ℂn-bundle over a smooth m-dimensional manifold without boundary. More specifically, we are concerned with first order sesquilinear forms, namely, those generating first order systems. Our

    更新日期:2020-03-05
  • Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-03-04
    Joscha Henheik; Stefan Teufel

    We first review the problem of a rigorous justification of Kubo’s formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect rests on the validity of Kubo’s formula for such systems, a connection that we review briefly as well. We then highlight an approach to linear response theory based

    更新日期:2020-03-04
  • Unitary propagators for N-body Schrödinger equations in external field
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-02-28
    Kenji Yajima

    We report our recent results on the existence and uniqueness of unitary propagators for N-particle Schrödinger equations which may be applied to most interesting problems in physics.

    更新日期:2020-02-28
  • Scattering on periodic metric graphs
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-02-13
    Evgeny Korotyaev; Natalia Saburova

    We consider the Laplacian on a periodic metric graph and obtain its decomposition into a direct fiber integral in terms of the corresponding discrete Laplacian. Eigenfunctions and eigenvalues of the fiber metric Laplacian are expressed explicitly in terms of eigenfunctions and eigenvalues of the corresponding fiber discrete Laplacian and eigenfunctions of the Dirichlet problem on the unit interval

    更新日期:2020-02-13
  • Global multiplicity bounds and spectral statistics for random operators
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-02-13
    Anish Mallick; Krishna Maddaly

    In this paper, we consider Anderson type operators on a separable Hilbert space where the random perturbations are finite rank and the random variables have full support on ℝ. We show that spectral multiplicity has a uniform lower bound whenever the lower bound is given on a set of positive Lebesgue measure on the point spectrum away from the continuous one. We also show a deep connection between the

    更新日期:2020-02-13
  • Generic nature of asymptotic completeness in dissipative scattering theory
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-02-07
    Jérémy Faupin

    We review recent results obtained in the scattering theory of dissipative quantum systems representing the long-time evolution of a system S interacting with another system S′ and susceptible of being absorbed by S′. The effective dynamics of S is generated by an operator of the form H=H0+V−iC∗C on the Hilbert space of the pure states of S, where H0 is the self-adjoint generator of the free dynamics

    更新日期:2020-02-07
  • The algebra of Wick polynomials of a scalar field on a Riemannian manifold
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-02-03
    Claudio Dappiaggi; Nicolò Drago; Paolo Rinaldi

    On a connected, oriented, smooth Riemannian manifold without boundary we consider a real scalar field whose dynamics is ruled by E, a second-order elliptic partial differential operator of Laplace type. Using the functional formalism and working within the framework of algebraic quantum field theory and of the principle of general local covariance, first we construct the algebra of locally covariant

    更新日期:2020-02-03
  • Random matrices with exchangeable entries
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-01-30
    Werner Kirsch; Thomas Kriecherbauer

    We consider ensembles of real symmetric band matrices with entries drawn from an infinite sequence of exchangeable random variables, as far as the symmetry of the matrices permits. In general, the entries of the upper triangular parts of these matrices are correlated and no smallness or sparseness of these correlations is assumed. It is shown that the eigenvalue distribution measures still converge

    更新日期:2020-01-30
  • On Howland time-independent formulation of CP-divisible quantum evolutions
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-01-14
    Krzysztof Szczygielski; Robert Alicki

    We extend Howland time-independent formalism to the case of completely positive and trace preserving dynamics of finite-dimensional open quantum systems governed by periodic, time-dependent Lindbladian in Weak Coupling Limit, expanding our result from previous papers. We propose the Bochner space of periodic, square integrable matrix-valued functions, as well as its tensor product representation, as

    更新日期:2020-01-14
  • (No) Wigner Theorem for C*-algebras
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-01-10
    Klaas Landsman; Kitty Rang

    Wigner’s Theorem states that bijections of the set 𝒫1(H) of one-dimensional projections on a Hilbert space H that preserve transition probabilities are induced by either a unitary or an anti-unitary operator on H (which is uniquely determined up to a phase). Since elements of 𝒫1(H) define pure states on the C*-algebra B(H) of all bounded operators on H (though typically not producing all of them)

    更新日期:2020-01-10
  • Asymptotic eigenfunctions for Schrödinger operators on a vector bundle
    Rev. Math. Phys. (IF 1.215) Pub Date : 2020-01-06
    Matthias Ludewig; Elke Rosenberger

    In the limit ℏ→0, we analyze a class of Schrödinger operators Hℏ=ℏ2L+ℏW+V⋅idℰ acting on sections of a vector bundle ℰ over a Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has a non-degenerate minimum at some point p∈M. We construct quasimodes of WKB-type near p for eigenfunctions associated with the low-lying eigenvalues of Hℏ. These

    更新日期:2020-01-06
  • Finite lifespan of solutions of the semilinear wave equation in the Einstein–de Sitter spacetime
    Rev. Math. Phys. (IF 1.215) Pub Date : 2019-12-20
    Anahit Galstian; Karen Yagdjian

    We examine the solutions of the semilinear wave equation, and, in particular, of the φq model of quantum field theory in the curved spacetime. More exactly, for 2

    更新日期:2019-12-20
  • Topological insulators and the Kane–Mele invariant: Obstruction and localization theory
    Rev. Math. Phys. (IF 1.215) Pub Date : 2019-12-09
    Severin Bunk; Richard J. Szabo

    We present homotopy theoretic and geometric interpretations of the Kane–Mele invariant for gapped fermionic quantum systems in three dimensions with time-reversal symmetry. We show that the invariant is related to a certain 4-equivalence which lends it an interpretation as an obstruction to a block decomposition of the sewing matrix up to non-equivariant homotopy. We prove a Mayer–Vietoris Theorem

    更新日期:2019-12-09
  • Spectral analysis of the spin-boson Hamiltonian with two bosons for arbitrary coupling and bounded dispersion relation
    Rev. Math. Phys. (IF 1.215) Pub Date : 2019-11-21
    Orif O. Ibrogimov

    We study the spectrum of the spin-boson Hamiltonian with two bosons for arbitrary coupling α>0 in the case when the dispersion relation is a bounded function. We derive an explicit description of the essential spectrum which consists of the so-called two- and three-particle branches that can be separated by a gap if the coupling is sufficiently large. It turns out, that depending on the location of

    更新日期:2019-11-21
  • Weighted quantum measurements
    Rev. Math. Phys. (IF 1.215) Pub Date : 2019-11-21
    Andrzej Łuczak; Rafał Wieczorek

    In the paper, the Belavkin weighted square root measurement in infinite dimension is investigated. The question of uniqueness of such measurement is analyzed and some estimates for the probability of detection are obtained. Moreover, the asymptotics of the probability of detection and the probability of failure are derived in the situation when the pure states approach an orthonormal basis. The results

    更新日期:2019-11-21
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