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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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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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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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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.
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Anyonic defect branes and conformal blocks in twisted equivariant differential (TED) K-theory Rev. Math. Phys. (IF 1.8) Pub Date : 2023-03-09 Hisham Sati, Urs Schreiber
We demonstrate that twisted equivariant differential K-theory of transverse complex curves accommodates exotic charges of the form expected of codimension=2 defect branes, such as of D7-branes in IIB/F-theory on 𝔸-type orbifold singularities, but also of their dual 3-brane defects of class-S theories on M5-branes. These branes have been argued, within F-theory and the AGT correspondence, to carry
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Cosimplicial meromorphic functions cohomology on complex manifolds Rev. Math. Phys. (IF 1.8) Pub Date : 2023-02-08 A. Zuevsky
Developing ideas of [B. L. Feigin, Conformal field theory and cohomologies of the Lie algebra of holomorphic vector fields on a complex curve, in Proc. Int. Congress of Mathematicians (Kyoto, 1990), Vols. 1 and 2 (Mathematical Society of Japan, Tokyo, 1991), pp. 71–85], we introduce canonical cosimplicial cohomology of meromorphic functions for infinite-dimensional Lie algebra formal series with prescribed
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Bogoliubov dynamics and higher-order corrections for the regularized Nelson model Rev. Math. Phys. (IF 1.8) Pub Date : 2023-01-09 Marco Falconi, Nikolai Leopold, David Mitrouskas, Sören Petrat
We study the time evolution of the Nelson model in a mean-field limit in which N nonrelativistic bosons weakly couple (with respect to the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove the convergence of the approximate wave function to the many-body wave function
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On Araki’s extension of the Jordan–Wigner transformation Rev. Math. Phys. (IF 1.8) Pub Date : 2023-01-05 Walter H. Aschbacher
In his seminal paper [On the XY-model on two-sided infinite chain, Publ. RIMS Kyoto Univ. 20 (1984) 277–296], Araki introduced an elegant extension of the Jordan–Wigner transformation which establishes a precise connection between quantum spin systems and Fermi lattice gases in one dimension in the so-called infinite system idealization of quantum statistical mechanics. His extension allows in particular
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Homotopy theory of net representations Rev. Math. Phys. (IF 1.8) Pub Date : 2023-01-04 Angelos Anastopoulos, Marco Benini
The homotopy theory of representations of nets of algebras over a (small) category with values in a closed symmetric monoidal model category is developed. We illustrate how each morphism of nets of algebras determines a change-of-net Quillen adjunction between the model categories of net representations, which is furthermore, a Quillen equivalence when the morphism is a weak equivalence. These techniques
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Anyonic topological order in twisted equivariant differential (TED) K-theory Rev. Math. Phys. (IF 1.8) Pub Date : 2022-12-06 Hisham Sati, Urs Schreiber
While the classification of noninteracting crystalline topological insulator phases by equivariant K-theory has become widely accepted, its generalization to anyonic interacting phases — hence to phases with topologically ordered ground states supporting topological braid quantum gates — has remained wide open. On the contrary, the success of K-theory with classifying noninteracting phases seems to
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C∗-extreme points of entanglement breaking maps Rev. Math. Phys. (IF 1.8) Pub Date : 2022-12-06 B. V. Rajarama Bhat, Repana Devendra, Nirupama Mallick, K. Sumesh
In this paper, we study the C∗-convex set of unital entanglement breaking (EB-)maps on matrix algebras. General properties and an abstract characterization of C∗-extreme points are discussed. By establishing a Radon–Nikodym-type theorem for a class of EB-maps we give a complete description of the C∗-extreme points. It is shown that a unital EB-map Φ:𝕄d1→𝕄d2 is C∗-extreme if and only if it has Choi-rank
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Quantum operations on conformal nets Rev. Math. Phys. (IF 1.8) Pub Date : 2022-12-06 Marcel Bischoff, Simone Del Vecchio, Luca Giorgetti
On a conformal net 𝒜, one can consider collections of unital completely positive maps on each local algebra 𝒜(I), subject to natural compatibility, vacuum preserving and conformal covariance conditions. We call quantum operations on 𝒜 the subset of extreme such maps. The usual automorphisms of 𝒜 (the vacuum preserving invertible unital *-algebra morphisms) are examples of quantum operations, and
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Dynamical evolution of entanglement in disordered oscillator systems Rev. Math. Phys. (IF 1.8) Pub Date : 2022-11-28 Houssam Abdul-Rahman
We study the non-equilibrium dynamics of a disordered quantum system consisting of harmonic oscillators in a d-dimensional lattice. If the system is sufficiently localized, we show that, starting from a broad class of initial product states that are associated with a tiling (decomposition) of the d-dimensional lattice, the dynamical evolution of entanglement follows an area law in all times. Moreover
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On thermodynamic and ultraviolet stability bounds for bosonic lattice QCD models in Euclidean dimensions d = 2,3,4 Rev. Math. Phys. (IF 1.8) Pub Date : 2022-11-28 Paulo A. Faria da Veiga, Michael O’Carroll
We prove thermodynamic and ultraviolet stable stability bounds for lattice scalar QCD quantum models, with multiflavor real or complex scalar Bose matter fields and a compact, connected gauge Lie group 𝒢=U(N), SU(N) with Lie algebra dimension D(N). Our models are defined on a finite hypercubic lattice Λ⊂aℤd, d=2,3,4, a∈(0,1], with L∈ℕ, even, sites on a side, Λs=Ld sites, and with free boundary conditions
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Lifting statistical structures Rev. Math. Phys. (IF 1.8) Pub Date : 2022-11-10 Katarzyna Grabowska, Janusz Grabowski, Marek Kuś, Giuseppe Marmo
In this paper, we consider some natural (functorial) lifts of geometric objects associated with statistical manifolds (metric tensor, dual connections, skewness tensor, etc.) to higher tangent bundles. It turns out that the lifted objects form again a statistical manifold structure, this time on the higher tangent bundles, with the only difference that the metric tensor is pseudo-Riemannian. What is
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Review and concrete description of the irreducible unitary representations of the universal cover of the complexified Poincaré group Rev. Math. Phys. (IF 1.8) Pub Date : 2022-11-07 Luigi M. Borasi
In this paper, we give a pedagogical presentation of the irreducible unitary representations of ℂ4⋊Spin(4,ℂ), that is, of the universal cover of the complexified Poincaré group ℂ4⋊SO(4,ℂ). These representations were first investigated by Roffman in 1967. We provide a modern formulation of his results together with some facts from the general Wigner–Mackey theory which are relevant in this context.
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Relative and quasi-entropies in semifinite von Neumann algebras Rev. Math. Phys. (IF 1.8) Pub Date : 2022-10-22 Andrzej Łuczak, Hanna Podsędkowska, Rafał Wieczorek
We prove that Araki’s relative entropy equals Umegaki’s information between normal states on semifinite von Neumann algebras, as well as derive formulae for quasi-entropies and Rényi’s relative entropy in semifinite von Neumann algebras, generalizing thus the results known in finite dimension. Our investigations rest on a thorough analysis of the relative modular operator in such an algebra.
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Limiting distribution of extremal eigenvalues of d-dimensional random Schrödinger operator Rev. Math. Phys. (IF 1.8) Pub Date : 2022-10-22 Kaito Kawaai, Yugo Maruyama, Fumihiko Nakano
We consider the Schrödinger operator with random decaying potential on ℓ2(Zd) and showed that, (i) Integrated Density of States (IDS) coincide with that of free Laplacian in general cases, (ii) the set of extremal eigenvalues, after rescaling, converges to an inhomogeneous Poisson process, under certain condition on the single-site distribution, and (iii) there are “border-line” cases, such that we
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Rigid body with rotors and reduction by stages Rev. Math. Phys. (IF 1.8) Pub Date : 2022-09-24 Miguel Á. Berbel, Marco Castrillón López
Rigid body with rotors is a widespread mechanical system modeled after the direct product SO(3)×𝕊1×𝕊1×𝕊1, which under mild assumptions is the symmetry group of the system. In this paper, the authors present and compare different Lagrangian reduction procedures: Euler–Poincaré reduction by the whole group and reduction by stages in different orders or using different connections. The exposition keeps
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A HC model with countable set of spin values: Uncountable set of Gibbs measures Rev. Math. Phys. (IF 1.8) Pub Date : 2022-09-24 U. A. Rozikov, F. H. Haydarov
We consider a hard core (HC) model with a countable set ℤ of spin values on the Cayley tree. This model is defined by a countable set of parameters λi>0,i∈ℤ∖{0}. For all possible values of parameters, we give limit points of the dynamical system generated by a function which describes the consistency condition for finite-dimensional measures. Also, we prove that every periodic Gibbs measure for the
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The second law of thermodynamics as a deterministic theorem for quantum spin systems Rev. Math. Phys. (IF 1.8) Pub Date : 2022-09-21 Walter F. Wreszinski
We review our approach to the second law of thermodynamics as a theorem asserting the growth of the mean (Gibbs–von Neumann) entropy of quantum spin systems undergoing automorphic (unitary) adiabatic transformations. Non-automorphic interactions with the environment, although known to produce on the average a strict reduction of the entropy of systems with finite number of degrees of freedom, are proved
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Criteria for the absolutely continuous spectral components of matrix-valued Jacobi operators Rev. Math. Phys. (IF 1.8) Pub Date : 2022-09-15 Fabrício Vieira Oliveira, Silas Luiz de Carvalho
We extend in this work the Jitomirskaya–Last inequality [Power-law subordinacy and singular spectra i. Half-line operators, Acta Math. 183 (1999) 171–189] and Last and Simon [Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators, Invent. Math. 135 (1999) 329–367] criterion for the absolutely continuous spectral component of a half-line Schrödinger
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ℛ(p,q)-deformed super Virasoro n-algebras Rev. Math. Phys. (IF 1.8) Pub Date : 2022-08-31 Fridolin Melong
In this paper, we construct the super Witt algebra and super Virasoro algebra in the framework of the ℛ(p,q)-deformed quantum algebras. Moreover, we perform the super ℛ(p,q)-deformed Witt n-algebra, the ℛ(p,q)-deformed Virasoro n-algebra and discuss the super ℛ(p,q)-Virasoro n-algebra (n even). Besides, we define and construct another super ℛ(p,q)-deformed Witt n-algebra and study a toy model for the
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Frobenius objects in the category of spans Rev. Math. Phys. (IF 1.8) Pub Date : 2022-08-29 Ivan Contreras, Molly Keller, Rajan Amit Mehta
We consider Frobenius objects in the category Span, where the objects are sets and the morphisms are isomorphism classes of spans of sets. We show that such structures are in correspondence with data that can be characterized in terms of simplicial sets. An interesting class of examples comes from groupoids. Our primary motivation is that Span can be viewed as a set-theoretic model for the symplectic
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Global theory of graded manifolds Rev. Math. Phys. (IF 1.8) Pub Date : 2022-08-24 Jan Vysoký
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on ℤ-graded variables which can either commute or anticommute, according to their degree. To obtain a consistent global description of graded manifolds, one resorts to sheaves of graded commutative
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Continuous dependence on the initial data in the Kadison transitivity theorem and GNS construction Rev. Math. Phys. (IF 1.8) Pub Date : 2022-08-06 Daniel Spiegel, Juan Moreno, Marvin Qi, Michael Hermele, Agnès Beaudry, Markus J. Pflaum
We consider how the outputs of the Kadison transitivity theorem and Gelfand–Naimark–Segal (GNS) construction may be obtained in families when the initial data are varied. More precisely, for the Kadison transitivity theorem, we prove that for any nonzero irreducible representation (ℋ,π) of a C∗-algebra 𝔄 and n∈ℕ, there exists a continuous function A:X→𝔄 such that π(A(x,y))xi=yi for all i∈{1,…,n}
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Real spectral triples on crossed products Rev. Math. Phys. (IF 1.8) Pub Date : 2022-08-06 Alessandro Rubin, Ludwik Dąbrowski
Given a spectral triple on a unital C*-algebra A and an equicontinuous action of a discrete group G on A, a spectral triple on the reduced crossed product C*-algebra A⋊rG was constructed by Hawkins, Skalski, White and Zacharias in [On spectral triples on crossed products arising from equicontinuous actions, Math. Scand. 113(2) (2013) 262–291], extending the construction by Belissard, Marcolli and Reihani
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Excitation spectrum of Bose gases beyond the Gross–Pitaevskii regime Rev. Math. Phys. (IF 1.8) Pub Date : 2022-08-03 Christian Brennecke, Marco Caporaletti, Benjamin Schlein
We consider Bose gases of N particles in a box of volume one, interacting through a repulsive potential with scattering length of order N−1+κ, for κ>0. Such regimes interpolate between the Gross–Pitaevskii and thermodynamic limits. Assuming that κ is sufficiently small, we determine the ground state energy and the low-energy excitation spectrum, up to errors vanishing in the limit N→∞.
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Absence of ground states in the renormalized massless translation-invariant Nelson model Rev. Math. Phys. (IF 1.8) Pub Date : 2022-08-03 Thomas Norman Dam, Benjamin Hinrichs
We consider a model for a massive uncharged non-relativistic particle interacting with a massless bosonic field, widely referred to as the Nelson model. It is well known that an ultraviolet renormalized Hamilton operator exists in this case. Further, due to translation-invariance, it decomposes into fiber operators. In this paper, we treat the renormalized fiber operators. We give a description of
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Quantum radiation from a classical point source Rev. Math. Phys. (IF 1.8) Pub Date : 2022-07-29 J. Dimock
We study the radiation of photons from a classical charged particle. We particularly consider a situation where the particle has a constant velocity in the distant past, then is accelerated, and then has a constant velocity in the distant future. Starting with no photons in the distant past we seek to characterize the quantum state of the photon field in the distant future. Working in the Coulomb gauge
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4-Manifold topology, Donaldson–Witten theory, Floer homology and higher gauge theory methods in the BV-BFV formalism Rev. Math. Phys. (IF 1.8) Pub Date : 2022-07-22 Nima Moshayedi
We study the behavior of Donaldson’s invariants of 4-manifolds based on the moduli space of anti-self-dual connections (instantons) in the perturbative field theory setting where the underlying source manifold has boundary. It is well-known that these invariants take values in the instanton Floer homology groups of the boundary 3-manifold. Gluing formulae for these constructions lead to a functorial
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Symmetric states for C∗-Fermi systems Rev. Math. Phys. (IF 1.8) Pub Date : 2022-07-18 Francesco Fidaleo
After introducing the infinite Fermi C∗-tensor product of a single ℤ2-graded C∗-algebra as an inductive limit, we systematically study the structure of the so-called symmetric states, that is those which are invariant under the group consisting of all finite permutations of a countable set. Among the obtained results, we mention the extension of De Finetti theorem which asserts that a symmetric state
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Markovian repeated interaction quantum systems Rev. Math. Phys. (IF 1.8) Pub Date : 2022-07-08 Jean-François Bougron, Alain Joye, Claude-Alain Pillet
We study a class of dynamical semigroups (𝕃n)n∈ℕ that emerge, by a Feynman–Kac type formalism, from a random quantum dynamical system (ℒωn∘⋯∘ℒω1(ρω0))n∈ℕ driven by a Markov chain (ωn)n∈ℕ. We show that the almost sure large time behavior of the system can be extracted from the large n asymptotics of the semigroup, which is in turn directly related to the spectral properties of the generator 𝕃. As
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One-matrix differential reformulation of two-matrix models Rev. Math. Phys. (IF 1.8) Pub Date : 2022-07-04 Joren Brunekreef, Luca Lionni, Johannes Thürigen
Differential reformulations of field theories are often used for explicit computations. We derive a one-matrix differential formulation of two-matrix models, with the help of which it is possible to diagonalize the one- and two-matrix models using a formula by Itzykson and Zuber that allows diagonalizing differential operators with respect to matrix elements of Hermitian matrices. We detail the equivalence
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Yamabe and gradient Yamabe solitons in the complex hyperbolic two-plane Grassmannians Rev. Math. Phys. (IF 1.8) Pub Date : 2022-06-23 Young Jin Suh
First, we want to give a complete classification of Yamabe solitons and gradient Yamabe solitons for real hypersurfaces in the complex hyperbolic two-plane Grassmannians G2*(ℂm+2). Next, as an application we also give a complete classification of quasi-Yamabe and gradient quasi-Yamabe solitons on real hypersurfaces in the complex hyperbolic two-plane Grassmannians G2*(ℂm+2).
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Free boson realization of the Dunkl intertwining operator in one dimension Rev. Math. Phys. (IF 1.8) Pub Date : 2022-06-23 Luc Vinet, Alexei Zhedanov
The operator that intertwines between the ℤ2-Dunkl operator and the derivative is shown to have a realization in terms of the oscillator operators in one dimension. This observation rests on the fact that the Dunkl intertwining operator maps the Hermite polynomials on the generalized Hermite polynomials.