Model of the effective separable potential in the problem of three one-dimensional quantum particlesThe goal of this paper is to construct an effective model for studying the asymptotic solution of the scattering problem of three one-dimensional quantum particles with finite (short-range)…Sergey B. Levin, Alexandr S. Bagmutov, Victor O. Toropov·May 19, 2024SaveLearn
Distribution of points on the real line under a class of repulsive potentialsIn a 1979 paper, Ventevogel and Nijboer showed that classical point particles interacting via the pair potential φ(x)=(1+x4)-1 are not equally spaced in their ground states in one…Roni Edwin·May 19, 2024SaveLearn
Symplectic duality via log topological recursionWe review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of x-y…Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski et al.·May 17, 2024SaveLearn
On pressureless Euler equation with external forceHodograph equations for the n-dimensional Euler equations with the constant pressure and external force linear in velocity are presented. They provide us with solutions of the Euler in implicit form…B. G. Konopelchenko, G. Ortenzi·May 17, 2024SaveLearn
Localization and unique continuation for non-stationary Schr\"odinger operators on the 2D latticeWe extend methods of Ding and Smart from their breakthrough paper in 2020 which showed Anderson localization for certain random Schr\"odinger operators on 2(Z2) via a quantitative…Omar Hurtado·May 17, 2024SaveLearn
Spectral analysis of Dirac operators for fermion scattering on topological solitons in the nonlinear O(3) σ-modelWe investigate the existence of discrete positive or negative energy ground states of the Dirac operator H which describe the fermion scattering on topological solitons in the nonlinear O(3)…Daiju Funakawa, Satoshi Okumura, Yuki Ueda·May 17, 2024SaveLearn
Segre surfaces and geometry of the Painlev\'e equationsIn this paper, we consider a six parameter family of affine Segre surfaces embedded in C6. For generic values of the parameters, this family is associated to the q-difference sixth…Nalini Joshi, Marta Mazzocco, Pieter Roffelsen·May 17, 2024SaveLearn
A systematic path to non-Markovian dynamics II: Probabilistic response of nonlinear multidimensional systems to Gaussian colored noise excitationThe probabilistic characterization of non-Markovian responses to nonlinear dynamical systems under colored excitation is an important issue, arising in many applications. Extending the…Gerassimos A. Athanassoulis, Nikolaos P. Nikoletatos-Kekatos, Konstantinos Mamis·May 16, 2024SaveLearn
Tetrahedron equation and Schur functionsThe tetrahedron equation introduced by Zamolodchikov is a three-dimensional generalization of the Yang-Baxter equation. Several types of solutions to the tetrahedron equation that have connections to…Shinsuke Iwao, Kohei Motegi, Ryo Ohkawa·May 16, 2024SaveLearn
Landscapes of integrable long-range spin chainsWe clarify how the elliptic integrable spin chain recently found by Matushko and Zotov (MZ) relates to various other known long-range spin chains. The limit q1 gives the elliptic spin chain of…Rob Klabbers, Jules Lamers·May 15, 2024SaveLearn
Clustering of higher order connected correlations in C* dynamical systemsIn the context of C* dynamical systems, we consider a locally compact group G acting by *-automorphisms on a C* algebra U of observables, and assume a state of U…Dimitrios Ampelogiannis, Benjamin Doyon·May 15, 2024SaveLearn
Monge-Ampere Geometry and the Eady ProblemChynoweth and Sewell proposed a mathematical model for an atmospheric front based on the singularities of the Legendre transformation between different pairs of dual variables. Drawing inspiration…Roberto D'Onofrio, Giovanni Ortenzi, Ian Roulstone·May 15, 2024SaveLearn
Spectral zeta function and ground state of quantum Rabi modelThe spectral zeta function of the quantum Rabi Hamiltonian is considered. It is shown that the spectral zeta function converges to the Riemann zeta function as the coupling constant goes to infinity.…Fumio Hiroshima, Tomoyuki Shirai·May 15, 2024SaveLearn
Construction of special Lagrangian submanifolds of the Taub-NUT manifold and the Atiyah-Hitchin manifoldWe construct special Lagrangian submanifolds of the Taub-NUT manifold and the Atiyah-Hitchin manifold by combining the generalized Legendre transform approach and the moment map technique. The…Masato Arai, Kurando Baba·May 15, 2024SaveLearn
On absolutely continuous spectrum for one-channel unitary operatorsIn this paper, we develop the radial transfer matrix formalism for unitary one-channel operators. This generalizes previous formalisms for CMV matrices and scattering zippers. We establish an analog…Olivier Bourget, Gregorio Moreno, Christian Sadel et al.·May 14, 2024SaveLearn
Quantum Integrable Systems arising from Separation of Variables on S3We study the family of quantum integrable systems that arise from separating the Schr\"odinger equation in all 6 separable orthogonal coordinates on the 3 sphere: ellipsoidal, prolate, oblate,…Sean Dawson, Holger Dullin·May 14, 2024SaveLearn
Commuting Clifford actionsIt shown that if a vector space carries commuting actions of two Clifford algebras, then the quadratic monomials using generators from either Clifford algebra determine a spinor representation of an…John W. Barrett·May 14, 2024SaveLearn
Ruijsenaars duality for B, C, D Toda chainsWe use the Hamiltonian reduction method to construct the Ruijsenaars dual systems to generalized Toda chains associated with the classical Lie algebras of types B, C, D. The dual systems turn out…Ivan Sechin, Mikhail Vasilev·May 14, 2024SaveLearn
The one-dimensional Coulomb Hamiltonian: Properties of its Birman-Schwinger operatorWe study the Birman-Schwinger operator for a self-adjoint realisation of the one-dimensional Hamiltonian with the Coulomb potential. We study both the case in which this Hamiltonian is defined on the…S. Fassari, M. Gadella, J. T. Lunardi et al.·May 14, 2024SaveLearn
Rogers-Ramanujan identities in Statistical MechanicsWe describe the story of the Rogers-Ramanujan identities; being known for 85 years and having about 130 pure mathematics proofs, suddenly entering physics when Rodney Baxter solved the Hard Hexagon…Geoffrey B. Campbell·May 14, 2024SaveLearn
Gaussian measure on the dual of U(N), random partitions, and topological expansion of the partition functionWe study a Gaussian measure with parameter q∈(0,1) on the dual of the unitary group of size N: we prove that a random highest weight under this measure is the coupling of two independent…Thibaut Lemoine, Mylène Maïda·May 14, 2024SaveLearn
On Long Range Ising Models with Random Boundary ConditionsWe consider polynomial long-range Ising models in one dimension, with ferromagnetic pair interactions decaying with power 2-α (for 0 ≤ α < 1), and prepared with randomly chosen…Eric O. Endo, Aernout C. D. van Enter, Arnaud Le Ny·May 14, 2024SaveLearn
Macroscopic Fluctuation Theory for Ginzburg-Landau dynamics with long range interactionsFocusing on a famous class of interacting diffusion processes called Ginzburg-Landau (GL) dynamics, we extend the Macroscopic Fluctuations Theory (MFT) to these systems in the case where the…Cédric Bernardin, Raphaël Chetrite·May 13, 2024SaveLearn
A Linear Prelle-Singer methodThe Prelle-Singer method allows determining an elementary first integral admitted by a polynomial vector field in the plane. It is a semi-algorithm whose nonlinear step consists of determining the…L. G. S. Duarte, H. S. Ferreira, L. A. C. P. da Mota·May 13, 2024SaveLearn
The fermionic massless modular HamiltonianWe provide an explicit expression for the modular hamiltonian of the von Neumann algebras associated to the unit double cone for the (fermionic) quantum field theories of the 2-component Weyl…Francesca La Piana, Gerardo Morsella·May 13, 2024SaveLearn