A reduction procedure for determining exact solutions of second order hyperbolic equationsIn this paper we develop a systematic reduction procedure for determining intermediate integrals of second order hyperbolic equations so that exact solutions of the second order PDEs under interest…Natale Manganaro, Alessandra Rizzo·May 6, 2024SaveLearn
On Wave-Like Differential Equations in General Hilbert Space. The Functional Analytic Investigation of Euler-Bernoulli Bending Vibrations of a Beam as an Application in Engineering ScienceWave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical…Reinhard Honegger, Michael Lauxmann, Barbara Priwitzer·May 6, 2024SaveLearn
Upper Bound for the Free Energy of Dilute Bose Gases at Low TemperatureWe consider a Bose gas at density > 0, interacting through a repulsive potential V ∈ L2 (R3) with scattering length a > 0. We prove an upper bound for the free…Florian Haberberger, Christian Hainzl, Benjamin Schlein et al.·May 6, 2024SaveLearn
The Ising Model Coupled to 2D Gravity: Higher-order Painlev\'e Equations/The (3,4) String EquationWe study a higher-order Painlev\'e-type equation, arising as a string equation of the 3rd order reduction of the KP hierarchy. This equation appears at the multi-critical point of the…Nathan Hayford·May 6, 2024SaveLearn
The Ising Model Coupled to 2D Gravity: Genus Zero Partition FunctionWe compute the genus 0 free energy for the 2-matrix model with quartic interactions, which acts as a generating function for the Ising model's partition function on a random, 4-regular, planar graph.…Maurice Duits, Nathan Hayford, Seung-Yeop Lee·May 6, 2024SaveLearn
Interface Modes in Honeycomb Topological Photonic Structures with Broken Reflection SymmetryIn this work, we present a mathematical theory for Dirac points and interface modes in honeycomb topological photonic structures consisting of impenetrable obstacles. Starting from a honeycomb…Wei Li, Junshan Lin, Jiayu Qiu et al.·May 6, 2024SaveLearn
Self-adjointness of unbounded time operatorsTime operators for an abstract semi-bounded self-adjoint operator H with purely discrete spectrum is considered. The existence of a bounded self-adjoint time operator T for H is known as…Fumio Hiroshima, Noriaki Teranishi·May 5, 2024SaveLearn
Rigged Hilbert Space formulation for quasi-Hermitian composite systemsThe discussion in this study delves into Dirac's bra-ket formalism for a quasi-Hermitian quantum composite system based on the rigged Hilbert space (RHS). We establish an RHS with a positive definite…Shousuke Ohmori·May 5, 2024SaveLearn
RKHS, Berezin and Odzijewicz-type quantizations on arbitrary compact smooth manifoldIn this article we define Berezin-type and Odzijewicz-type quantizations on compact smooth manifolds. The method is we embed the smooth manifold of real dimension n into CPn and induce…Rukmini Dey·May 5, 2024SaveLearn
A note on hidden classes in spinor classificationThe Lounesto classification is a well-established scheme for categorizing spinors based on their physical content, which are determined by their associated bilinear forms. It consists of six disjoint…R. J. Bueno Rogerio, R. T. Cavalcanti, C. H. Coronado Villalobos et al.·May 4, 2024SaveLearn
Bootstrapping cascaded random matrix models: correlations in permutations of matrix productsRandom matrix theory is a useful tool in the study of the physics of multiple scattering systems, often striking a balance between computation speed and physical rigour. Propagation of waves through…Niall Byrnes, Gary R. W. Greaves, Matthew R. Foreman·May 4, 2024SaveLearn
Deformation maps of quasi-twilled Lie algebrasIn this paper, we provide a unified approach to study the cohomology theories and deformation theories of various types of operators in the category of Lie algebras, including modified r-matrices,…Jun Jiang, Yunhe Sheng, Rong Tang·May 4, 2024SaveLearn
On finite-dimensional smoothed-particle Hamiltonian reductions of the Vlasov equationThe inclusion of spatial smoothing in finite-dimensional particle-based Hamiltonian reductions of the Vlasov equation are considered. In the context of the Vlasov-Poisson equation (and other…William Barham, Philip J. Morrison·May 3, 2024SaveLearn
Supersymmetric Quantum Mechanics on a noncommutative plane through the lens of deformation quantizationA gauge invariant mathematical formalism based on deformation quantization is outlined to model an N=2 supersymmetric system of a spin 1/2 charged particle placed in a nocommutative…Md. Rafsanjany Jim, S. Hasibul Hassan Chowdhury·May 3, 2024SaveLearn
Spectral density of complex eigenvalues and associated mean eigenvector self-overlaps at the edge of elliptic Ginibre ensemblesWe consider the density of complex eigenvalues, (z), and the associated mean eigenvector self-overlaps, O(z), at the spectral edge of N × N real and complex elliptic Ginibre…Mark J. Crumpton, Tim R. Würfel·May 3, 2024SaveLearn
k-Fold Gaussian Random Matrix Ensembles I: Forcing Structure into Random MatricesRandom Matrix Theory is a powerful tool in applied mathematics. Three canonical models of random matrix distributions are the Gaussian Orthogonal, Unitary and Symplectic Ensembles. For matrix…Michael Brodskiy, Owen L. Howell·May 2, 2024SaveLearn
The Correlation Energy of the Electron Gas in the Mean-Field RegimeWe prove a rigorous lower bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of singular interactions, including the Coulomb potential. Combined with…Martin Ravn Christiansen, Christian Hainzl, Phan Thành Nam·May 2, 2024SaveLearn
Q-Boson model and relations with integrable hierarchiesThis work investigates the intricate relationship between the q-boson model, a quantum integrable system, and classical integrable systems such as the Toda and KP hierarchies. Initially, we analyze…Thiago Araujo·May 2, 2024SaveLearn
Multiplicatively Ordered and Directed Hybrid Jordan-Lie SuperalgebraA new algebra, hitherto not encountered in the usual Lie algebraic varieties or supervarieties, is introduced. The paper explores the rich and novel structure of the algebra, and it compares it on…Ioannis Raptis·May 2, 2024SaveLearn
Continuous extension of the discrete shift translations on one-dimensional quantum lattice systemsWe study the continuous extension of discrete shift translations on one-dimensional quantum lattice systems.Hajime Moriya, Heide Narnhofer·May 2, 2024SaveLearn
IR-fixed Euclidean vacuum for linearized gravity on de Sitter spaceWe consider the Euclidean vacuum for linearized gravity on the global de Sitter space, obtained from the Euclidean Green's function on the 4-sphere. We use the notion of Calder\'on projectors to…Christian Gérard, Michał Wrochna·May 1, 2024SaveLearn
Reverse Lieb-Thirring inequality for the half-line matrix Schr\"odinger operatorWe prove a reverse Lieb-Thirring inequality with a sharp constant for the matrix Schr\"odinger equation on the half-line.Ricardo Weder·May 1, 2024SaveLearn
Universality of the second correlation function of the deformed Ginibre ensembleWe study the deformed complex Ginibre ensemble H=A0+H0, where H0 is the complex matrix with iid Gaussian entries, and A0 is some general n× n matrix (it can be random and in this…Ievgenii Afanasiev, Mariya Shcherbina, Tatyana Shcherbina·May 1, 2024SaveLearn
Large gap probabilities of complex and symplectic spherical ensembles with point chargesWe consider n eigenvalues of complex and symplectic induced spherical ensembles, which can be realised as two-dimensional determinantal and Pfaffian Coulomb gases on the Riemann sphere under the…Sung-Soo Byun, Seongjae Park·May 1, 2024SaveLearn
An elliptic fibration arising from the Lagrange top and its monodromyThis paper is to investigate an elliptic fibration over CP2 arising from the Lagrange top from the viewpoint of complex algebraic geometry. The description of the discriminant locus of…Genki Ishikawa·May 1, 2024SaveLearn