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Mathematical Physics papers — page 233

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Quantum Wasserstein isometries on the qubit state space
We describe Wasserstein isometries of the quantum bit state space with respect to distinguished cost operators. We derive a Wigner-type result for the cost operator involving all the Pauli matrices:…
György Pál Gehér, József Pitrik, Tamás Titkos et al.Apr 29, 2022
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Limiting distribution of extremal eigenvalues of d-dimensional random Schrödinger operator
We consider Schrödinger operator with random decaying potential on 2 ( Zd) and showed that, (i) IDS coincides with that of free Laplacian in general cases, and (ii) the set of extremal…
Kaito Kawaai, Yugo Maruyama, Fumihiko NakanoApr 29, 2022
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Implementing Bogoliubov Transformations Beyond the Shale-Stinespring Condition
We provide two extensions of a dense subspace of Fock space, such that Bogoliubov transformations become implementable on them, even though they violate the Shale-Stinespring condition, so they are…
Sascha LillApr 28, 2022
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On operator estimates in homogenization of non-local operators of convolution type
The paper studies a bounded symmetric operator A in L2(Rd) with (A u) (x) = -d-2 ∫Rd a((x-y)/)…
A. Piatnitski, V. Sloushch, T. Suslina et al.Apr 28, 2022
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Limit Theorems on the Mesoscopic Scale for the Anderson Model
In this paper, we study eigenvalue fluctuations of the finite volume Anderson model in the mesoscopic scale. We carry out this study in a regime of exponential localization and prove a central limit…
Yoel GrinshponApr 28, 2022
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Reflection positivity and infrared bounds for quantum spin systems
The method of reflection positivity and infrared bounds allows to prove the occurrence of phase transitions in systems with continuous symmetries. We review the method in the context of quantum spin…
Jakob E. Björnberg, Daniel UeltschiApr 27, 2022
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Large-scale geometry obstructs localization
We explain the coarse geometric origin of the fact that certain spectral subspaces of topological insulator Hamiltonians are delocalized, in the sense that they cannot admit an orthonormal basis of…
Matthias Ludewig, Guo Chuan ThiangApr 27, 2022
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2-Spinors via Linear Algebra
We give a streamlined account of 2-spinors, up to and including the Dirac equation, using little more than the resources of linear algebra. We prove that the Dirac bundle is isomorphic to the…
Roger PlymenApr 27, 2022
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Higher rank 1+1 integrable Landau-Lifshitz field theories from associative Yang-Baxter equation
We propose a construction of 1+1 integrable Heisenberg-Landau-Lifshitz type equations in the glN case. The dynamical variables are matrix elements of N× N matrix S with the property…
K. Atalikov, A. ZotovApr 26, 2022
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On higher Br\'ezin-Gross-Witten tau-functions
In this paper, we consider the higher Br\'ezin--Gross--Witten tau-functions, given by the matrix integrals. For these tau-functions we construct the canonical Kac--Schwarz operators, quantum spectral…
Alexander Alexandrov, Saswati DharaApr 26, 2022
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Formal exponentials and linearisations of QP-manifolds
We define formal exponential maps for any graded manifold as maps from the formal tangent bundle (that we also define) into the graded manifold. We show that each such map uniquely determines and is…
Alex S. ArvanitakisApr 26, 2022
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Chern-Simons theory, link invariants and the Askey-Wilson algebra
The occurrence of the Askey-Wilson (AW) algebra in the SU(2) Chern-Simons (CS) theory and in the Reshetikhin-Turaev (RT) link invariant construction with quantum algebra Uq(su2) is…
Nicolas Crampé, Luc Vinet, Meri ZaimiApr 26, 2022
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Mathematical multi-scale model of water purification
In this work we consider a mathematical model of the water treatment process and determine the effective characteristics of this model. At the microscopic length scale we describe our model in terms…
A. Piatnitski, A. Shamaev, E. ZhizhinaApr 26, 2022
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Gaps labeling theorem for the Bubble-diamond self-similar graphs
Motivated by the appearance of fractals in several areas of physics, especially in solid state physics and the physics of aperiodic order, and in other sciences, including the quantum information…
Elizabeth Melville, Gamal Mograby, Nikhil Nagabandi et al.Apr 25, 2022
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Decomposition of enveloping algebras of simple Lie algebras and their related polynomial algebras
The decomposition problem of the enveloping algebra of a simple Lie algebra is reconsidered combining both the analytical and the algebraic approach, showing its relation with the internal labelling…
Rutwig Campoamor-Stursberg, Ian MarquetteApr 25, 2022
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Towards a Geometry and Analysis for Bayesian Mechanics
In this paper, a simple case of Bayesian mechanics under the free energy principle is formulated in axiomatic terms. We argue that any dynamical system with constraints on its dynamics necessarily…
Dalton A R SakthivadivelApr 25, 2022
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Effective quantum Hamiltonian in thin domains with non-homogeneity
We consider the Laplacian with a non-homogeneous metric in a tubular neighbourhood of a compact hypersurface in the Euclidean space of arbitrary dimension, subject to Neumann boundary conditions. It…
Romana KvasnickovaApr 25, 2022
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Geometrical aspects of contact mechanical systems and field theories
Many important theories in modern physics can be stated using differential geometry. Symplectic geometry is the natural framework to deal with autonomous Hamiltonian mechanics. This admits several…
Xavier Rivas GuijarroApr 25, 2022
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Breather solution of non-linear Klein-Gordon equation
A technique for obtaining an approximate breather solution of the Klein-Gordon equation is presented. A breather solution of the equation describing the propagation of nonlinear waves in a…
D. V. Zav'yalov, V. I. Konchenkov, S. V. KryuchkovApr 24, 2022
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Parameter and q asymptotics of Lq-norms of hypergeometric orthogonal polynomials
The three canonical families of the hypergeometric orthogonal polynomials (Hermite, Laguerre and Jacobi) control the physical wavefunctions of the bound stationary states of a great deal of quantum…
Nahual Sobrino, J. S. DehesaApr 24, 2022
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An affine Weyl group characterization of polynomial Heisenberg algebras
We study deformations of the harmonic oscillator algebra known as polynomial Heisenberg algebras (PHAs), and establish a connection between them and extended affine Weyl groups of type A(1)m,…
V. S. Morales-SalgadoApr 23, 2022
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Grothendieck's Dessins d'Enfants in a Web of Dualities. III
We identify the dessin partition function with the partition function of the Laguerre unitary ensemble (LUE). Combined with the result due to Cunden et al on the relationship between the LUE…
Di Yang, Jian ZhouApr 23, 2022
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Action of vectorial Lie superalgebras on some split supermanifolds
The "curved" super Grassmannian is the supervariety of subsupervarieties of purely odd dimension k in a~supervariety of purely odd dimension n, unlike the "usual" super Grassmannian which is the…
Arkady OnishchikApr 23, 2022
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Spectral Theorem approach to the Characteristic Function of Quantum Observables II
We compute the resolvent of the anti-commutator operator XP+PX and of the quantum harmonic oscillator Hamiltonian operator 12(X2+P2). Using Stone's formula for finding the spectral…
Andreas BoukasApr 22, 2022
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A Note on the Gibbsian Representation of the Gradient of a Vector Field
In this note, we provide a important considerations of a familiar topic: the gradient of a vector field. The gradient of a vector field is a common quantity represented in continuum mechanics.…
Brian D. Wood, Peeter Joot, Stephen WhitakerApr 21, 2022
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