Quot scheme and deformation quantizationLet X be a compact connected Riemann surface, and let Q(r,d) denote the quot scheme parametrizing the torsion quotients of O rX of degree d. Given a projective…Indranil Biswas·Jun 18, 2024SaveLearn
Asymptotic behaviour of determinants through the expansion of the Moyal star productWe work out a generalization of the Szeg\"o limit theorems on the determinant of large matrices. We focus on matrices with nonzero leading principal minors and elements that decay to zero…Maurizio Fagotti, Vanja Marić·Jun 18, 2024SaveLearn
Classical and quantum KMS states on spin lattice systemsWe study the classical and quantum KMS conditions within the context of spin lattice systems. Specifically, we define a strict deformation quantization (SDQ) for a S2-valued spin lattice…Nicolò Drago, Lorenzo Pettinari, Christiaan J. F. van de Ven·Jun 18, 2024SaveLearn
Scaling limit of the ground state Bethe roots for the inhomogeneous XXZ spin-12 chainIt is known that for the Heisenberg XXZ spin-12 chain in the critical regime, the scaling limit of the vacuum Bethe roots yields an infinite set of numbers that coincide with the energy…Sascha Gehrmann, Gleb A. Kotousov, Sergei L. Lukyanov·Jun 17, 2024SaveLearn
Pluriharmonic solutions to Yang-Mills equations: a C*-algebras approachThis partially expository paper provides a view of Yang-Mills equations from the perspective of complex variables, operator theory, and C*-algebras. Through operator-valued pluriharmonic and…Marius Beceanu, Sachin Munshi, Rongwei Yang·Jun 17, 2024SaveLearn
Reflection Positivity and Chern-Simons Functional IntegralsWe show that a mathematical version of the formal Chern-Simons functional integral of Witten for manifolds equipped with a reflection may be constructed in terms of a reflection positive functional,…Jonathan Weitsman·Jun 17, 2024SaveLearn
Quantum interpretation of lattice pathsIn the 1980s, Viennot developed a combinatorial approach to studying mixed moments of orthogonal polynomials using Motzkin paths. Recently, an alternative combinatorial model for these mixed moments…Bhargavi Jonnadula, Jonathan P. Keating·Jun 17, 2024SaveLearn
A Hamiltonian approach to the gradient-flow equations in information geometryWe have studied the gradient-flow equations in information geometry from a point-particle perspective. Based on the motion of a null (or light-like) particle in a curved space, we have rederived the…Tatsuaki Wada, Antonio M. Scarfone·Jun 17, 2024SaveLearn
Determination of the Hamiltonian from the Equations of Motion with Illustration from ExamplesIn this paper, we study the determination of Hamiltonian from a given equations of motion. It can be cast into a problem of matrix factorization after reinterpretation of the system as first-order…Chung-Ru Lee·Jun 16, 2024SaveLearn
Kac-Moody and Virasoro algebras on the two-sphere and the two-torusWe particularise the construction of generalised Kac-Moody algebras associated to compact real manifolds to the case of the two-torus T2 and the two-sphere S2. It is shown…Rutwig Campoamor-Stursberg, Michel Rausch de Traubenberg·Jun 15, 2024SaveLearn
Bifurcation sequences in the secular 3D planetary 3-Body problem: a geometric approachWe implement the geometric method proposed in ([9], [3], [16]) to analytically predict the sequence of bifurcations leading to a change of stability and/or the appearance of new periodic orbits in…Rita Mastroianni, Antonella Marchesiello, Christos Efthymiopoulos et al.·Jun 14, 2024SaveLearn
An infinite-rank Lie algebra associated to SL(2, R) and SL(2, R)/U(1)We construct a generalised notion of Kac-Moody algebras using smooth maps from the non-compact manifolds M=SL(2, R) and M= SL(2, R)/U(1) to a finite-dimensional…Rutwig Campoamor-Stursberg, Alessio Marrani, Michel Rausch de Traubenberg·Jun 14, 2024SaveLearn
Mc'Kean's transformation for 3-rd order operatorsWe consider a non-self-adjoint third order operator (y''+py)'+py'+qy with 1-periodic coefficients p,q. This operator is the L-operator in the Lax pair for the good Boussinesq equation on the…Andrey Badanin, Evgeny Korotyaev·Jun 14, 2024SaveLearn
Ground state energy of a dilute Bose gas with three-body hard-core interactionsWe consider a gas of bosons interacting through a three-body hard-core potential in the thermodynamic limit. We derive an upper bound on the ground state energy of the system at the leading order…Lukas Junge, François Louis Antoine Visconti·Jun 13, 2024SaveLearn
Optimizing the auxetic behavior of anisotropic laminatesAnisotropic laminates with a negative Poisson's ratio for at least some directions are called auxetic. In this paper, we consider the conditions for optimizing the auxeticity of an orthotropic…Paolo Vannucci·Jun 12, 2024SaveLearn
Alternative representation of Magnus series by exact proper operator exponentIn this report the emphasis is on an alternative representation of the Magnus series by proper operator (matrix) exponential solutions to differential equations (systems), both linear and nonlinear…Yu. N. Kosovtsov·Jun 12, 2024SaveLearn
Bessel potentials and Green functions on pseudo-Euclidean spacesWe review properties of Bessel potentials, that is, inverse Fourier transforms of (regularizations of) 1(m2+p2)μ2 on a pseudoEuclidean space with signature (q,d-q). We…Jan Dereziński, Bartłomiej Sikorski·Jun 12, 2024SaveLearn
Infinite-dimensional Frobenius Manifolds and Extensions of Genus-Zero Whitham HierarchiesIn this paper we construct a class of infinite-dimensional Frobenius manifolds in the spaces of pairs of meromorphic functions defined on certain regions of the Riemann sphere. For such Frobenius…Shilin Ma, Chao-Zhong Wu, Dafeng Zuo·Jun 12, 2024SaveLearn
Effective Polaron Dynamics of an Impurity Particle Interacting with a Fermi GasWe study the quantum dynamics of a homogeneous ideal Fermi gas coupled to an impurity particle on a three-dimensional box with periodic boundary condition. For large Fermi momentum kF, we…Duc Viet Hoang, Peter Pickl·Jun 12, 2024SaveLearn
Bifurcation analysis of figure-eight choreography in the three-body problem based on crystallographic point groupsThe bifurcation of figure-eight choreography is analyzed by its symmetry group based on the variational principle of the action. The irreducible representations determine the symmetry and the…Hiroshi Fukuda, Hiroshi Ozaki·Jun 11, 2024SaveLearn
Quantum MEP hydrodynamical model for charge transportA well known procedure to get quantum hydrodynamical models for charge transport is to resort to the Wigner equations and deduce the hierarchy of the moment equations as in the semiclassical…V. D. Camiola, V. Romano, G. Vitanza·Jun 11, 2024SaveLearn
A numerical model for time-multiplexed Ising machines based on delay-line oscillatorsIsing machines (IM) have recently been proposed as unconventional hardware-based computation accelerators for solving NP-hard problems. In this work, we present a model for a time-multiplexed IM…Roman V. Ovcharov, Victor H. González, Artem Litvinenko et al.·Jun 11, 2024SaveLearn
Regularized quantum motion in a bounded set: Hilbertian aspectsIt is known that the momentum operator canonically conjugated to the position operator for a particle moving in some bounded interval of the line (with Dirichlet boundary conditions) is not…Fabio Bagarello, Jean-Pierre Gazeau, Camillo Trapani·Jun 11, 2024SaveLearn
Landscape estimates of the integrated density of states for Jacobi operators on graphsWe show the integrated density of states for a variety of Jacobi operators on graphs, such as the Anderson model and random hopping models on graphs with Gaussian heat kernel bounds, can be estimated…Laura Shou, Wei Wang, Shiwen Zhang·Jun 10, 2024SaveLearn
n Distinguishable Particles on the Real Line interacting via Two Body Delta PotentialsThis paper studies a system of n ∈ N: \, n ≥ 2 non-relativistic, spinless quantum particles moving on the real line and interacting via a two-body delta potential. The Hamiltonian of…Antonio Moscato·Jun 10, 2024SaveLearn