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Perturbation theory and canonical coordinates in celestial mechanics Rev. Math. Phys. (IF 1.8) Pub Date : 2024-04-17 Gabriella Pinzari
KAM theory owes most of its success to its initial motivation: the application to problems of celestial mechanics. The masterly application was offered by Arnold in the 60s who worked out a theorem, that he named the “Fundamental Theorem” (FT), especially designed for the planetary problem. However, FT could be really used at that purpose only when, about 50 years later, a set of coordinates constructively
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Boltzmann’s mean entropy formula for unbounded spin systems Rev. Math. Phys. (IF 1.8) Pub Date : 2024-04-17 Takahiro Kajisa
In this paper, we rigorously prove Boltzmann’s entropy formula S=klogW in classical unbounded spin systems. By restricting our consideration to negatively interacting super-stable potentials, we prove the existence of pressure and the concavity of micro-canonical entropy corresponding to logW. Notably, the lattice φν4 model becomes a feasible example through the exploitation of the physical equivalence
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Feynman checkers: External electromagnetic field and asymptotic properties Rev. Math. Phys. (IF 1.8) Pub Date : 2024-04-13 Fedor Ozhegov
In this paper, we study Feynman checkers, one of the most elementary models of electron motion. It is also known as a one-dimensional quantum walk or an Ising model at an imaginary temperature. We add the simplest non-trivial electromagnetic field and find the limits of the resulting model for small lattice step and large time, analogous to the results by Narlikar from 1972 and Grimmet–Jason–Scudo
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Some contributions to k-contact Lagrangian field equations, symmetries and dissipation laws Rev. Math. Phys. (IF 1.8) Pub Date : 2024-04-13 Xavier Rivas, Modesto Salgado, Silvia Souto
It is well known that k-contact geometry is a suitable framework to deal with non-conservative field theories. In this paper, we study some relations between solutions of the k-contact Euler–Lagrange equations, symmetries, dissipation laws and Newtonoid vector fields. We review the k-contact Euler–Lagrange equations written in terms of k-vector fields and sections and provide new results relating the
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Some closer estimations for Tsallis relative operator entropy Rev. Math. Phys. (IF 1.8) Pub Date : 2024-04-13 Ismail Nikoufar, Mehdi Kanani Arpatapeh
In this paper, we find some new and refined bounds for the Tsallis relative operator entropy. We give the lower and upper bounds for the Tsallis relative operator entropy such that the lower bound is an ascending sequence that ascends to the Tsallis relative operator entropy and the upper bound is a descending sequence that descends to the Tsallis relative operator entropy. Moreover, we present some
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Complex translation methods and its application to resonances for quantum walks Rev. Math. Phys. (IF 1.8) Pub Date : 2024-04-10 Kenta Higuchi, Hisashi Morioka
In this paper, some properties of resonances for multi-dimensional quantum walks are studied. Resonances for quantum walks are defined as eigenvalues of complex translated time evolution operators in the pseudo momentum space. For some typical cases, we show some results of existence or nonexistence of resonances. One is a perturbation of an elastic scattering of a quantum walk which is an analogue
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Light cones for open quantum systems in the continuum Rev. Math. Phys. (IF 1.8) Pub Date : 2024-04-10 Sébastien Breteaux, Jérémy Faupin, Marius Lemm, Dong Hao Ou Yang, Israel Michael Sigal, Jingxuan Zhang
We consider Markovian open quantum dynamics (MOQD) in the continuum. We show that, up to small-probability tails, the supports of quantum states evolving under such dynamics propagate with finite speed in any finite-energy subspace. More precisely, we prove that if the initial quantum state is localized in space, then any finite-energy part of the solution of the von Neumann–Lindblad equation is approximately
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Homotopical foundations of parametrized quantum spin systems Rev. Math. Phys. (IF 1.8) Pub Date : 2024-03-16 Agnès Beaudry, Michael Hermele, Juan Moreno, Markus J. Pflaum, Marvin Qi, Daniel D. Spiegel
In this paper, we present a homotopical framework for studying invertible gapped phases of matter from the point of view of infinite spin lattice systems, using the framework of algebraic quantum mechanics. We define the notion of quantum state types. These are certain lax-monoidal functors from the category of finite-dimensional Hilbert spaces to the category of topological spaces. The universal example
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Lattice Green functions for pedestrians: Exponential decay Rev. Math. Phys. (IF 1.8) Pub Date : 2024-03-12 Wojciech Dybalski, Alexander Stottmeister, Yoh Tanimoto
The exponential decay of lattice Green functions is one of the main technical ingredients of the Bałaban’s approach to renormalization. We give here a self-contained proof, whose various ingredients were scattered in the literature. The main sources of exponential decay are the Combes–Thomas method and the analyticity of the Fourier transforms. They are combined using a renormalization group equation
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A result about the classification of quantum covariance matrices based on their eigenspectra Rev. Math. Phys. (IF 1.8) Pub Date : 2024-03-11 Arik Avagyan
The set of covariance matrices of a continuous-variable quantum system with a finite number of degrees of freedom is a strict subset of the set of real positive-definite matrices (PDMs) due to Heisenberg’s uncertainty principle. This has the implication that, in general, not every orthogonal transform of a quantum covariance matrix (CM) produces a PDM that obeys the uncertainty principle. A natural
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Browder operators on quaternionic Hilbert space Rev. Math. Phys. (IF 1.8) Pub Date : 2024-03-06 Sarita Kumari, Preeti Dharmarha
In this paper, we study the notions of Browder operator and Browder S-spectrum of bounded right linear operator defined over the right quaternionic Hilbert space. Some properties of Browder operator and stability of the ascent, descent and Browder S-spectrum have been investigated in the right quaternionic setting. We also characterize the property of invariant Browder operators and study the spectral
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Quantizing graphs, one way or two? Rev. Math. Phys. (IF 1.8) Pub Date : 2024-03-05 Jon Harrison
Quantum graphs were introduced to model free electrons in organic molecules using a self-adjoint Hamiltonian on a network of intervals. A second graph quantization describes wave propagation on a graph by specifying scattering matrices at the vertices. A question that is frequently raised is the extent to which these models are the same or complementary. In particular, are all energy-independent unitary
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On uniform decay of the Maxwell fields on black hole space-times Rev. Math. Phys. (IF 1.8) Pub Date : 2024-03-02 Sari Ghanem
In this paper, we study the Maxwell equations in the domain of outer-communication of the Schwarzschild black hole. We prove that if the middle components of the non-stationary solutions of the Maxwell equations verify a Morawetz-type estimate supported on a compact region in space around the trapped surface, then the components of the Maxwell fields decay uniformly in the entire exterior of the Schwarzschild
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Analytical solutions to the 1D compressible isothermal Navier–Stokes equations with Maxwell’s law Rev. Math. Phys. (IF 1.8) Pub Date : 2024-03-02 Jianwei Dong, Lijuan Bo
In this paper, we present some analytical solutions to the one-dimensional compressible isothermal Navier–Stokes equations with Maxwell’s law in the real line. First, we construct two analytical solutions by using a self-similar ansatz, one blows up in finite time and the other exists globally-in-time. Second, we construct two global analytical solutions with different large initial data by using a
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Schottky cohomology for rank two bosonic vertex operator algebra Rev. Math. Phys. (IF 1.8) Pub Date : 2024-02-29 A. Zuevsky
Using the Schottky procedure of forming a genus g Riemann surface by attaching handles to the Riemann sphere, we construct coboundary operators and corresponding cohomology for the double complexes of rational functions associated to a particular example of the rank two bosonic vertex operator algebra V.
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Gibbs states and their classical limit Rev. Math. Phys. (IF 1.8) Pub Date : 2024-01-29 Christiaan J. F. van de Ven
A continuous bundle of C∗-algebras provides a rigorous framework to study the thermodynamic limit of quantum theories. If the bundle admits the additional structure of a strict deformation quantization (in the sense of Rieffel) one is allowed to study the classical limit of the quantum system, i.e. a mathematical formalism that examines the convergence of algebraic quantum states to probability measures
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On topology changes in quantum field theory and quantum gravity Rev. Math. Phys. (IF 1.8) Pub Date : 2024-01-11 Benjamin Schulz
Two singularity theorems can be proven if one attempts to let a Lorentzian cobordism interpolate between two topologically distinct manifolds. On the other hand, Cartier and DeWitt-Morette have given a rigorous definition for quantum field theories (QFTs) by means of path integrals. This paper uses their results to study whether QFTs can be made compatible with topology changes. We show that path integrals
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On spectral and scattering theory for one-body quantum systems in crossed constant electric and magnetic fields Rev. Math. Phys. (IF 1.8) Pub Date : 2024-01-11 Tadayoshi Adachi, Yuta Tsujii
In this paper, we study the spectral and scattering theory on the Hamiltonians which govern one-body quantum systems in crossed constant electric and magnetic fields. As one of the spectral features of the Hamiltonians, we show the absence of bound states of theirs under some appropriate conditions on the potentials. Moreover, by using the limiting absorption principle for the Hamiltonians, we give
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Geometric background for the Teukolsky equation revisited Rev. Math. Phys. (IF 1.8) Pub Date : 2024-01-04 Pascal Millet
The aim of this review paper is to revisit the geometric framework of the Teukolsky equation in a form that is suitable for analysts working on this equation. We introduce spinor bundles, the Newman–Penrose formalism and the Geroch–Held–Penrose (GHP) formalism. In particular, we develop the case of Kerr spacetimes, for which we provide detailed computations.
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Conformal super Virasoro algebra: Matrix model and quantum deformed algebra Rev. Math. Phys. (IF 1.8) Pub Date : 2024-01-04 Fridolin Melong
In this paper, we construct the super Virasoro algebra with an arbitrary conformal dimension Δ from the generalized ℛ(p,q)-deformed quantum algebra and investigate the ℛ(p,q)-deformed super Virasoro algebra with the particular conformal dimension Δ=1. Furthermore, we perform the ℛ(p,q)-conformal Virasoro n-algebra, the ℛ(p,q)-conformal super Virasoro n-algebra (n-even) and discuss a toy model for the
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Kolmogorov extension theorem for non-probability measures on Cayley trees Rev. Math. Phys. (IF 1.8) Pub Date : 2023-12-30 F. H. Haydarov
In this paper, we shall discuss the extendability of probability and non-probability measures on Cayley trees to a σ-additive measure on Borel fields which has a fundamental role in the theory of Gibbs measures.
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Spectral asymptotics of elliptic operators on manifolds Rev. Math. Phys. (IF 1.8) Pub Date : 2023-12-28 Ivan G. Avramidi
The study of spectral properties of natural geometric elliptic partial differential operators acting on smooth sections of vector bundles over Riemannian manifolds is a central theme in global analysis, differential geometry and mathematical physics. Instead of studying the spectrum of a differential operator L directly one usually studies its spectral functions, that is, spectral traces of some functions
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Complete infinitesimal prolongation of the Riemann–Liouville and Caputo derivatives Rev. Math. Phys. (IF 1.8) Pub Date : 2023-12-28 Felix S. Costa, Junior C. A. Soares, Gastão S. F. Frederico, J. Vanterler da C. Sousa, S. Jarosz
This paper presents the infinitesimal prolongation to Riemann–Liouville and Caputo fractional derivatives without the restrictive lower limit fixed in the integrals, when applicated to the transformation group. The properties are presented, and the examples are illustrated along with the symmetry to fractional derivative criteria.
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Connections on Lie groupoids and Chern–Weil theory Rev. Math. Phys. (IF 1.8) Pub Date : 2023-12-21 Indranil Biswas, Saikat Chatterjee, Praphulla Koushik, Frank Neumann
Let 𝕏=[X1⇉X0] be a Lie groupoid equipped with a connection, given by a smooth distribution ℋ⊂TX1 transversal to the fibers of the source map. Under the assumption that the distribution ℋ is integrable, we define a version of de Rham cohomology for the pair (𝕏,ℋ), and we study connections on principal G-bundles over (𝕏,ℋ) in terms of the associated Atiyah sequence of vector bundles. We also discuss
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Lorentzian manifolds: A characterization with a type of semi-symmetric non-metric connection Rev. Math. Phys. (IF 1.8) Pub Date : 2023-12-08 Young Jin Suh, Sudhakar Kumar Chaubey, Mohammad Nazrul Islam Khan
This paper characterizes the Lorentzian manifolds endowed with a semi-symmetric non-metric ρ-connection (briefly, ssnmρc). First, the existence of semi-symmetric non-metric connection (ssnmc) on Lorentzian manifold is established, and it is shown that an n-dimensional Lorentzian manifold equipped with an ssnmρc is a generalized Robertson–Walker spacetime. We also establish the condition for a Lorentzian
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Topological aspects of matters and Langlands program Rev. Math. Phys. (IF 1.8) Pub Date : 2023-12-07 Kazuki Ikeda
The Langlands program is a vast mathematical projection linking number theory and geometry. In high-energy physics, a connection with mirror symmetry has been suggested in string theory, but it has been little studied in low-energy physics. In the framework of the Langlands program, we present a unified description of the integer and fractional quantum Hall effect and the duality found in the fractal
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Notes on the type classification of von Neumann algebras Rev. Math. Phys. (IF 1.8) Pub Date : 2023-12-07 Jonathan Sorce
This paper provides an explanation of the type classification of von Neumann algebras, which has made many appearances in the recent work on entanglement in quantum field theory and quantum gravity. The goal is to bridge a gap in the literature between resources that are too technical for the non-expert reader, and resources that seek to explain the broad intuition of the theory without giving precise
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On a category of V-structures for foliations Rev. Math. Phys. (IF 1.8) Pub Date : 2023-12-02 A. Zuevsky
For a foliation ℱ of a smooth complex manifold, we introduce the category 𝒞 of V-structures associated to a vertex operator algebra V and the category of its modules. The main result consists of the construction of V-structures and canonicity proof of 𝒞 on ℱ.
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Sign-changing solutions for a weighted Schrödinger–Kirchhoff equation with double exponential nonlinearities growth Rev. Math. Phys. (IF 1.8) Pub Date : 2023-12-02 Sami Baraket, Rima Chetouane, Rached Jaidane, Wafa Mtaouaa
This work is devoted to the existence of least energy nodal solutions for a nonlocal weighted Schrödinger–Kirchhoff problem, under boundary Dirichlet condition in the unit ball B of ℝ2. The nonlinearity of the equation is assumed to have double exponential growth in view of Trudinger–Moser type inequalities. By using the constrained minimization in Nehari set, the quantitative deformation Lemma and
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Determination of black holes by boundary measurements Rev. Math. Phys. (IF 1.8) Pub Date : 2023-11-29 G. Eskin
For a wave equation with time-independent Lorentzian metric consider an initial-boundary value problem in ℝ×Ω, where x0∈ℝ is the time variable and Ω is a bounded domain in ℝn. Let Γ⊂∂Ω be a subdomain of ∂Ω. We say that the boundary measurements are given on ℝ×Γ if we know the Dirichlet and Neumann data on ℝ×Γ. The inverse boundary value problem consists of recovery of the metric from the boundary measurements
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Boundary triples and Weyl functions for Dirac operators with singular interactions Rev. Math. Phys. (IF 1.8) Pub Date : 2023-11-09 Jussi Behrndt, Markus Holzmann, Christian Stelzer-Landauer, Georg Stenzel
In this paper, we develop a systematic approach to treat Dirac operators Aη,τ,λ with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions of strengths η,τ,λ∈ℝ, respectively, supported on points in ℝ, curves in ℝ2, and surfaces in ℝ3 that is based on boundary triples and their associated Weyl functions. First, we discuss the one-dimensional case which also serves as a motivation
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Universality in low-dimensional BCS theory Rev. Math. Phys. (IF 1.8) Pub Date : 2023-10-31 Joscha Henheik, Asbjørn Bækgaard Lauritsen, Barbara Roos
It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density
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Quantum conditional entropy based on local quantum Bernoulli noises Rev. Math. Phys. (IF 1.8) Pub Date : 2023-10-31 Qi Han, Shuai Wang, Lijie Gou, Rong Zhang
Quantum noise has always been an important issue in the field of quantum information transmission. As the localization of quantum noise, local quantum Bernoulli noises (LQBNs) have attracted extensive attention in recent years. In this paper, the quantum conditional entropy based on LQBNs is deeply discussed, and a new definition of quantum conditional entropy is given. Then we find that this quantum
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Non-existence of spontaneous symmetry breakdown of time-translation symmetry on general quantum systems: Any macroscopic order parameter moves not! Rev. Math. Phys. (IF 1.8) Pub Date : 2023-10-27 Hajime Moriya
The Kubo–Martin–Schwinger (KMS) condition is a well-founded general definition of equilibrium states on quantum systems. The time invariance property of equilibrium states is one of its basic consequences. From the time invariance of any equilibrium state it follows that the spontaneous breakdown of time-translation symmetry is impossible. Moreover, triviality of the temporal long-range order is derived
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Quantum f-divergences via Nussbaum–Szkoła distributions and applications to f-divergence inequalities Rev. Math. Phys. (IF 1.8) Pub Date : 2023-09-22 George Androulakis, Tiju Cherian John
The main result in this paper shows that the quantum f-divergence of two states is equal to the classical f-divergence of the corresponding Nussbaum–Szkoła distributions. This provides a general framework for studying certain properties of quantum entropic quantities using the corresponding classical entities. The usefulness of the main result is illustrated by obtaining several quantum f-divergence
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Lower bounds on the energy of the Bose gas Rev. Math. Phys. (IF 1.8) Pub Date : 2023-09-15 Søren Fournais, Theotime Girardot, Lukas Junge, Leo Morin, Marco Olivieri
We present an overview of the approach to establish a lower bound to the ground state energy for the dilute, interacting Bose gas in a periodic box. In this paper, the size of the box is larger than the Gross–Pitaevskii length scale. The presentation includes both the two- and three-dimensional cases, and catches the second-order correction, i.e. the Lee–Huang–Yang term. The calculation on a box of
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Geometrically induced spectral properties of soft quantum waveguides and layers Rev. Math. Phys. (IF 1.8) Pub Date : 2023-09-07 Pavel Exner
We present a review of recent results about a class of Schrödinger operators usually called soft quantum waveguides, with the focus on relations between their spectral properties and the geometry of the confinement. We also mention a number of open problems in this area.
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Correlation inequalities for the uniform eight-vertex model and the toric code model Rev. Math. Phys. (IF 1.8) Pub Date : 2023-08-21 J. E. Björnberg, B. Lees
We investigate connections between four models in statistical physics and probability theory: (1) the toric code model of Kitaev, (2) the uniform eight-vertex model, (3) random walk on a hypercube, and (4) a classical Ising model with four-body interaction. As a consequence of our analysis (and of the GKS-inequalities for the Ising model) we obtain correlation inequalities for the toric code model
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Correlation energy of weakly interacting Fermi gases Rev. Math. Phys. (IF 1.8) Pub Date : 2023-08-21 Benjamin Schlein
In this paper, based on [N. Benedikter, P. T. Nam, M. Porta, B. Schlein and R. Seiringer. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime, Commun. Math. Phys. 374(3) (2020) 2097–2150; N. Benedikter, P. T. Nam, M. Porta, B. Schlein and R. Seiringer, Correlation energy of a weakly interacting Fermi gas, Invent. Math.225(3) (2021) 885–979; N. Benedikter, M. Porta
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Hopf algebroids from non-commutative bundles Rev. Math. Phys. (IF 1.8) Pub Date : 2023-08-08 Xiao Han, Giovanni Landi, Yang Liu
We present two classes of examples of Hopf algebroids associated with non-commutative principal bundles. The first comes from deforming the principal bundle while leaving unchanged the structure Hopf algebra. The second is related to deforming a quantum homogeneous space; this needs a careful deformation of the structure Hopf algebra in order to preserve the compatibilities between the Hopf algebra
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Geometric properties of special orthogonal representations associated to exceptional Lie superalgebras Rev. Math. Phys. (IF 1.8) Pub Date : 2023-08-03 Philippe Meyer
From an octonion algebra 𝕆 over a field k of characteristic not two or three, we show that the fundamental representation Im(𝕆) of the derivation algebra Der(𝕆) and the spinor representation 𝕆 of 𝔰𝔬(Im(𝕆)) are special orthogonal representations. They have particular geometric properties coming from their similarities with binary cubics and we show that the covariants of these representations
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On a new proof of the Okuyama–Sakai conjecture Rev. Math. Phys. (IF 1.8) Pub Date : 2023-08-01 Di Yang, Qingsheng Zhang
Okuyama and Sakai [JT supergravity and Brézin–Gross–Witten tau-function, J. High Energy Phys.2020 (2020) 160] gave a conjectural equality for the higher genus generalized Brézin–Gross–Witten (BGW) free energies. In a recent work [D. Yang and Q. Zhang, On the Hodge-BGW correspondence, preprint (2021), arXiv:2112.12736], we established the Hodge-BGW correspondence on the relationship between certain
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Peeling for tensorial wave equations on Schwarzschild spacetime Rev. Math. Phys. (IF 1.8) Pub Date : 2023-07-28 Truong Xuan Pham
In this paper, we establish the asymptotic behavior along outgoing and incoming radial geodesics, i.e. the peeling property for the tensorial Fackerell–Ipser and spin ±1 Teukolsky equations on Schwarzschild spacetime. Our method combines a conformal compactification with vector field techniques to prove the two-side estimates of the energies of tensorial fields through the future and past null infinity
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Quantum polynomials from deformed quantum algebras: Probability distributions, generating functions and difference equations Rev. Math. Phys. (IF 1.8) Pub Date : 2023-07-27 Mahouton Norbert Hounkonnou, Fridolin Melong
In this paper, we provide a novel generalization of quantum orthogonal polynomials from ℛ(p,q)-deformed quantum algebras introduced in earlier works. We construct related quantum Jacobi polynomials and their probability distribution, factorial moments, recurrence relation, and governing difference equation. Surprisingly, these polynomials obey non-conventional recurrence relations. Particular cases
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Quasi-free states on a class of algebras of multicomponent commutation relations Rev. Math. Phys. (IF 1.8) Pub Date : 2023-07-24 Eugene Lytvynov, Nedal Othman
Multicomponent commutations relations (MCRs) describe plektons, i.e. multicomponent quantum systems with a generalized statistics. In such systems, exchange of quasiparticles is governed by a unitary matrix Q(x1,x2) that depends on the position of quasiparticles. For such an exchange to be possible, the matrix must satisfy several conditions, including the functional Yang–Baxter equation. The aim of
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Feynman checkers: Number-theoretic properties Rev. Math. Phys. (IF 1.8) Pub Date : 2023-07-21 F. Kuyanov, A. Slizkov
We study Feynman checkers, an elementary model of electron motion introduced by Feynman. In this model, a checker moves on a checkerboard, and we count the turns. Feynman checkers are also known as a one-dimensional quantum walk. We prove some new number-theoretic results in this model, for example, sign alternation of the real and imaginary parts of the electron wave function in a specific area. All
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Properties of Fredholm, Weyl and Jeribi essential S-spectra in a right quaternionic Hilbert space Rev. Math. Phys. (IF 1.8) Pub Date : 2023-07-19 Preeti Dharmarha, Sarita Kumari
The paper aims to extend the concept of Fredholm, Weyl and Jeribi essential spectra in the quaternionic setting. Furthermore, some properties and stability of the corresponding spectra of Fredholm and Weyl operators have been investigated in this setting. To achieve the goal, a characterization of the sum of two invariant bounded linear operators has been obtained in order to explore various properties
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Local eigenvalue statistics for higher-rank Anderson models after Dietlein–Elgart Rev. Math. Phys. (IF 1.8) Pub Date : 2023-07-17 Samuel Herschenfeld, Peter D. Hislop
We use the method of eigenvalue level spacing developed by Dietlein and Elgart [Level spacing and Poisson statistics for continuum random Schrödinger operators, J. Eur. Math. Soc. (JEMS)23(4) (2021) 1257–1293] to prove that the local eigenvalue statistics (LES) for the Anderson model on ℤd, with uniform higher-rank m≥2, single-site perturbations, is given by a Poisson point process with intensity measure
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Positive solutions for fractional Kirchhoff–Schrödinger–Poisson system with steep potential well Rev. Math. Phys. (IF 1.8) Pub Date : 2023-07-15 Hui Jian, Qiaocheng Zhong, Li Wang
In this paper, we deal with the following fractional Kirchhoff–Schrödinger–Poisson system: (a+b[u]s2)(−Δ)su+λV(x)u+μϕu=|u|p−2uin ℝ3,(−Δ)tϕ=u2in ℝ3, where s∈34,1,t∈(0,1),20 is a constant, b,λ,μ are positive parameters, V(x) represents a potential well with the bottom V−1(0). By applying the truncation technique and the parameter-dependent compactness lemma, we first prove the existence of positive solutions
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The Witten index for one-dimensional split-step quantum walks under the non-Fredholm condition Rev. Math. Phys. (IF 1.8) Pub Date : 2023-06-30 Yasumichi Matsuzawa, Akito Suzuki, Yohei Tanaka, Noriaki Teranishi, Kazuyuki Wada
It is recently shown that a split-step quantum walk possesses a chiral symmetry, and that a certain well-defined index can be naturally assigned to it. The index is a well-defined Fredholm index if and only if the associated unitary time-evolution operator has spectral gaps at both +1 and −1. In this paper, we extend the existing index formula for the Fredholm case to encompass the non-Fredholm case
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Symmetries in non-relativistic quantum electrodynamics Rev. Math. Phys. (IF 1.8) Pub Date : 2023-06-29 David Hasler, Markus Lange
We define symmetries in non-relativistic quantum electrodynamics, which have the physical interpretation of rotation, parity, and time reversal symmetry. We collect transformation properties related to these symmetries in Fock space representation as well as in the Schrödinger representation. As an application, we generalize and improve theorems about Kramers’ degeneracy in non-relativistic quantum
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External gauge field-coupled quantum dynamics: Gauge choices, Heisenberg algebra representations and gauge invariance in general, and the Landau problem in particular Rev. Math. Phys. (IF 1.8) Pub Date : 2023-06-21 Jan Govaerts
Even though its classical equations of motion are then left invariant, when an action is redefined by an additive total derivative or divergence term (in time, in the case of a mechanical system) such a transformation induces non-trivial consequences for the system’s canonical phase space formulation. This is even more true and then in more subtle ways for the canonically quantized dynamics, with,
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On Tsirelson pairs of C∗-algebras Rev. Math. Phys. (IF 1.8) Pub Date : 2023-06-21 Isaac Goldbring, Bradd Hart
We introduce the notion of a Tsirelson pair of C∗-algebras, which is a pair of C∗-algebras for which the space of quantum strategies obtained by using states on the minimal tensor product of the pair is dense in the space of quantum strategies obtained by using states on the maximal tensor product. We exhibit a number of examples of such pairs that are “nontrivial” in the sense that the minimal tensor
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Quantum Markov semigroup for open quantum system interacting with quantum Bernoulli noises Rev. Math. Phys. (IF 1.8) Pub Date : 2023-06-05 Lu Zhang, Caishi Wang
Quantum Bernoulli noises (QBNs) refer to the annihilation and creation operators acting on the space 𝔥 of square integrable Bernoulli functionals, which satisfy the canonical anti-commutation relation (CAR) in equal time. In this paper, we consider the Markov evolution of an open quantum system interacting with QBNs. Let 𝒦 be the system space of an open quantum system interacting with QBNs. Then
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Reduction cohomology of Riemann surfaces Rev. Math. Phys. (IF 1.8) Pub Date : 2023-05-16 A. Zuevsky
We study the algebraic conditions leading to the chain property of complexes for vertex operator algebra n-point functions (with their convergence assumed) with differential being defined through reduction formulas. The notion of the reduction cohomology of Riemann surfaces is introduced. Algebraic, geometrical, and cohomological meanings of reduction formulas are clarified. A counterpart of the Bott–Segal
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Framed 𝔼n-algebras from quantum field theory Rev. Math. Phys. (IF 1.8) Pub Date : 2023-05-16 Chris Elliott, Owen Gwilliam
This paper addresses the following question: given a topological quantum field theory on ℝn built from an action functional, when is it possible to globalize the theory so that it makes sense on an arbitrary smooth oriented n-manifold? We study a broad class of topological field theories — those of AKSZ type — and obtain an explicit condition for the vanishing of the framing anomaly, i.e. the obstruction
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Geometry of almost contact metrics as an almost ∗-η-Ricci–Bourguignon solitons Rev. Math. Phys. (IF 1.8) Pub Date : 2023-05-12 Santu Dey, Young Jin Suh
In this paper, we give some characterizations by considering almost ∗-η-Ricci–Bourguignon soliton as a Kenmotsu metric. It is shown that if a Kenmotsu metric endows a ∗-η-Ricci–Bourguignon soliton, then the curvature tensor R with the soliton vector field V is given by the expression (ℒVR)(V1,ξ)ξ=2𝜗{V1(r)ξ−V1(Dr)+ξ(Dr)−ξ(r)ξ−Dr}. Next, we show that if an almost Kenmotsu manifold such that ξ belongs
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Painlevé equations, integrable systems and the stabilizer set of Virasoro orbit Rev. Math. Phys. (IF 1.8) Pub Date : 2023-05-11 José F. Cariñena, Partha Guha, Manuel F. Rañada
We study a geometrical formulation of the nonlinear second-order Riccati equation (SORE) in terms of the projective vector field equation on S1, which in turn is related to the stability algebra of Virasoro orbit. Using Darboux integrability method, we obtain the first integral of the SORE and the results are applied to the study of its Lagrangian and Hamiltonian descriptions. Using these results,
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Large N two-dimensional Yang–Mills fields for the spectral behavior of Brownian particles and relativistic many-body systems Rev. Math. Phys. (IF 1.8) Pub Date : 2023-05-10 Timothy Ganesan
This work explores the spectral behavior of interacting many-body systems — gravitating dust solutions (galaxy formations and black hole clusters) and Brownian fluids. The eigenvalue dynamics of these systems are then represented by the two-dimensional Yang–Mills field (i.e. spectral projection). The interacting particles in the many-body systems are associated with random matrices of dimensions, N
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The canonical BV Laplacian on half-densities Rev. Math. Phys. (IF 1.8) Pub Date : 2023-04-27 Alberto S. Cattaneo
This is a didactical review on the canonical BV Laplacian on half-densities.