The spectrum properties of an integrable G2 invariant vertex modelThis paper is concerned with the study of properties of the exact solution of the fundamental integrable G2 vertex model. The model R-matrix and respective spin chain are presented in terms of…M. J. Martins·Jan 14, 2023SaveLearn
Recovering the shape of a quantum tree by two spectraWe show how to find the shape of an equilateral tree using the spectra of the Neumann and the Dirichlet problems generated by the Sturm-Liouville equation. In case of snowflake trees the spectra of…Vyacheslav Pivovarchik·Jan 14, 2023SaveLearn
Clarkson-McLeod solutions of the fourth Painlev\'e equation and the parabolic cylinder-kernel determinantThe Clarkson-McLeod solutions of the fourth Painlev\'e equation behave like Dα-122(2x) as x→ +∞, where is some real constant and…Jun Xia, Shuai-Xia Xu, Yu-Qiu Zhao·Jan 14, 2023SaveLearn
Mehler-Fock transforms and retarded radiative Green functions on hyperbolic and spherical spacesWe develop the theory of causal radiation Green functions on hyperbolic and hyperspherical spaces using a constructive approach based on generalized Mehler-Fock transforms. This approach focuses for…Loyal Durand·Jan 13, 2023SaveLearn
Universality in low-dimensional BCS theoryIt is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature and the critical temperature Tc is (approximately) given by a universal constant, independent…Joscha Henheik, Asbjørn Bækgaard Lauritsen, Barbara Roos·Jan 13, 2023SaveLearn
From Kraus Operators to the Stinespring Form of Quantum Maps: An Alternative Construction for Infinite DimensionsWe present an alternative (constructive) proof of the statement that for every completely positive, trace-preserving map there exists an auxiliary Hilbert space K in a pure state…Frederik vom Ende·Jan 13, 2023SaveLearn
A Causal Formulation of Dissipative Relativistic Fluid Dynamics with or without DiffusionThe article proposes a causal five-field formulation of dissipative relativistic fluid dynamics as a quasilinear symmetric hyperbolic system of second order. The system is determined by four…Heinrich Freistuhler·Jan 13, 2023SaveLearn
Higher order first integrals of autonomous non-Riemannian dynamical systemsWe consider autonomous holonomic dynamical systems defined by equations of the form qa=-bca(q) qbqc -Qa(q), where abc(q) are the…Antonios Mitsopoulos, Michael Tsamparlis, Aniekan Magnus Ukpong·Jan 13, 2023SaveLearn
High-Order SUSY-QM, the Quantum XP Model and zeroes of the Riemann Zeta functionMaking use of the first- and second-order algorithms of supersymmetric quantum mechanics (SUSY-QM), we construct quantum mechanical Hamiltonians whose spectra are related to the zeroes of the Riemann…Juan D García-Muñoz, A Raya, Y Concha-S·Jan 13, 2023SaveLearn
Complete characterization of nontrivial local conservation laws and nonexistence of local Hamiltonian structures for generalized Infeld--Rowlands equationWe characterize all cases when a certain natural generalization of the Infeld--Rowlands equation admits nontrivial local conservation laws of any order, and give explicit form of these conservation…Jakub Vašíček·Jan 12, 2023SaveLearn
Gaussian fluctuations in the Equipartition Principle for Wigner matricesThe total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the…Giorgio Cipolloni, László Erdős, Joscha Henheik et al.·Jan 12, 2023SaveLearn
Progress on the study of the Ginibre ensembles II: GinOE and GinSEThis is part II of a review relating to the three classes of random non-Hermitian Gaussian matrices introduced by Ginibre in 1965. While part I restricted attention to the GinUE (Ginibre unitary…Sung-Soo Byun, Peter J. Forrester·Jan 12, 2023SaveLearn
Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansionWe prove an upper bound on the ground state energy of the dilute spin-polarized Fermi gas capturing the leading correction to the kinetic energy resulting from repulsive interactions. One of the main…Asbjørn Bækgaard Lauritsen, Robert Seiringer·Jan 12, 2023SaveLearn
Miura-reciprocal transformations and localizable Poisson pencilsWe show that the equivalence classes of deformations of localizable semisimple Poisson pencils of hydrodynamic type with respect to the action of the Miura-reciprocal group contain a local…P. Lorenzoni, S. Shadrin, R. Vitolo·Jan 11, 2023SaveLearn
3D Bosons and W1+∞ algebraIn this paper, we consider 3D Young diagrams with at most N layers in z-axis direction, which can be constructed by N 2D Young diagrams on slice z=j, j=1,2,·s, N from the Yang-Baxter…Na Wang, Ke Wu·Jan 11, 2023SaveLearn
Spin glass phase at zero temperature in the Edwards-Anderson modelMean field spin glass models have undergone substantial mathematical development, but finite dimensional short range spin glasses remain much less understood. This paper proves several rigorous zero…Sourav Chatterjee·Jan 10, 2023SaveLearn
Blobbed topological recursion from extended loop equationsWe consider the N× N Hermitian matrix model with measure dμE,λ(M)=1Z (-λ N4 tr(M4)) dμE,0(M), where dμE,0 is the Gaussian measure…Alexander Hock, Raimar Wulkenhaar·Jan 10, 2023SaveLearn
A Q-operator for open spin chains II: boundary factorizationOne of the features of Baxter's Q-operators for many closed spin chain models is that all transfer matrices arise as products of two Q-operators with shifts in the spectral parameter. In the…Alec Cooper, Bart Vlaar, Robert Weston·Jan 10, 2023SaveLearn
A universal framework for entanglement detection under group symmetryOne of the most fundamental questions in quantum information theory is PPT-entanglement of quantum states, which is an NP-hard problem in general. In this paper, however, we prove that all PPT…Sang-Jun Park, Yeong-Gwang Jung, Jeongeun Park et al.·Jan 10, 2023SaveLearn
The singularities of Selberg- and Dotsenko-Fateev-like integralsWe discuss the meromorphic continuation of certain hypergeometric integrals modeled on the Selberg integral, including the 3-point and 4-point functions of BPZ's minimal models of 2D CFT as described…Ethan Sussman·Jan 10, 2023SaveLearn
Convergence rates for defect modes in large finite resonator arraysWe show that defect modes in infinite systems of resonators have corresponding modes in finite systems which converge as the size of the system increases. We study the generalized capacitance matrix…Habib Ammari, Bryn Davies, Erik Orvehed Hiltunen·Jan 9, 2023SaveLearn
Gaudin Hamiltonians on unitarizable modules over classical Lie (super)algebrasLet M be a tensor product of unitarizable irreducible highest weight modules over the Lie (super)algebra G, where G is gl(m|n), osp(2m|2n) or…Wan Keng Cheong, Ngau Lam·Jan 9, 2023SaveLearn
Exceptional points for associated Legendre functions of the second kindWe consider the complex plane structure of the associated Legendre function of the second kind Q-1/2-K(). We find that for any noninteger value for K…Tianye Liu, Daniel A. Norman, Philip D. Mannheim·Jan 8, 2023SaveLearn
Relegation-free closed-form perturbation theory and the domain of secular motions in the Restricted 3-Body ProblemWe propose a closed-form (i.e. without expansion in the orbital eccentricities) scheme for computations in perturbation theory in the restricted three-body problem (R3BP) when the massless particle…Mattia Rossi, Christos Efthymiopoulos·Jan 8, 2023SaveLearn
Exact Hydrodynamic Manifolds for the Linear Boltzmann BGK Equation I: Spectral TheoryWe perform a complete spectral analysis of the linear three-dimensional Boltzmann BGK operator resulting in an explicit transcendental equation for the eigenvalues. Using the theory of finite-rank…Florian Kogelbauer, Ilya Karlin·Jan 8, 2023SaveLearn