The spectral ζ-function for quasi-regular Sturm--Liouville operatorsIn this work we analyze the spectral ζ-function associated with the self-adjoint extensions, TA,B, of quasi-regular Sturm--Liouville operators that are bounded from below. By utilizing the…Guglielmo Fucci, Mateusz Piorkowski, Jonathan Stanfill·Sep 11, 2024SaveLearn
Les Houches lecture notes on topological recursionYou may have seen the words "topological recursion" mentioned in papers on matrix models, Hurwitz theory, Gromov-Witten theory, topological string theory, knot theory, topological field theory, JT…Vincent Bouchard·Sep 10, 2024SaveLearn
Limits of spectral measures for linearly bounded and for Poisson distributed random potentialsWe show the existence of infinite volume limits of resolvents and spectral measures for a class of Schroedinger operators with linearly bounded potentials. We then apply this result to Schroedinger…David Hasler, Jannis Koberstein·Sep 10, 2024SaveLearn
Magnetic Dirac operator in strips submitted to strong magnetic fieldsWe consider the magnetic Dirac operator on a curved strip whose boundary carries the infinite mass boundary condition. When the magnetic field is large, we provide the reader with accurate estimates…Loïc Le Treust, Julien Royer, Nicolas Raymond·Sep 10, 2024SaveLearn
Mathematical foundations of phonons in incommensurate materialsIn some models, periodic configurations can be shown to be stable under, both, global 2 or local perturbations. This is not the case for aperiodic media. The specific class of aperiodic media…Michael Hott, Alexander B. Watson, Mitchell Luskin·Sep 10, 2024SaveLearn
Nonholonomic momentum map reduction and a Chaplygin-type foliationThis paper presents a set-up for momentum map reduction of nonholonomic systems with symmetries, extending previous constructions in [3,25], based on the existence of certain conserved quantities and…Paula Balseiro, Danilo Machado Tereza·Sep 9, 2024SaveLearn
Correlation functions of the six-vertex IRF model and its quantum spin chainWe consider the interaction-round-a-face version of the isotropic six-vertex model. The associated spin chain is made of two coupled Heisenberg spin chains with different boundary twists. The phase…T. S. Tavares, G. A. P. Ribeiro·Sep 9, 2024SaveLearn
Exact Bethe quantum numbers of the massive XXZ chain in the two down-spin sectorEvery solution of the Bethe ansatz equations (BAE) is characterized by a set of quantum numbers called the Bethe quantum numbers, which are fundamental for evaluating it numerically. We rigorously…Takashi Imoto, Tetsuo Deguchi·Sep 9, 2024SaveLearn
The emptiness formation probability, and representations for nonlocal correlation functions, of the 20-vertex modelWe study the emptiness formation probability, along with various representations for nonlocal correlation functions, of the 20-vertex model. In doing so, we leverage previous arguments for…Pete Rigas·Sep 9, 2024SaveLearn
The Dirac Equation Near Centenary: a Contemporary Introduction to the Dirac Equation ConsiderationMore then 35 approaches to the Dirac equation derivation are presented. The various physical principles and mathematical methods are used. A review of well-known and not enough known contributions to…V. M. Simulik·Sep 9, 2024SaveLearn
Infinite-Length Limit of Spectral Curves and Inverse ScatteringIntegrability equips models of theoretical physics with efficient methods for the exact construction of useful states and their evolution. Relevant tools for classical integrable field models in one…Niklas Beisert, Kunal Gupta·Sep 8, 2024SaveLearn
Dual conformal invariant kinematics and folding of Grassmannian cluster algebrasGrassmannian manifolds (4,n) are closely related to the kinematic space of n-particle scattering processes in D=4, and their combinatorial and geometric structures have played an important…Jian-Rong Li, Changjian Su, Qinglin Yang·Sep 8, 2024SaveLearn
Spin-charge separation for paired Dirac fermions in (1+1) dimensionsWe study Dirac fermions at finite density coupled to a complex pairing field assumed to obey scalar field theory with quartic self-repulsion. The bulk of our work develops the mathematics that…Laith H. Haddad·Sep 7, 2024SaveLearn
A highly accurate procedure for computing globally optimal Wannier functions in one-dimensional crystalline insulatorsA standard task in solid state physics and quantum chemistry is the computation of localized molecular orbitals known as Wannier functions. In this manuscript, we propose a new procedure for…Abinand Gopal, Hanwen Zhang·Sep 6, 2024SaveLearn
The atmospheric Ekman spiral for piecewise-uniform eddy viscosityWe investigate the boundary-value problem of atmospheric Ekman flows with piecewise-uniform eddy viscosity. In addition we present a method for finding more general solutions by considering eddy…Eduard Stefanescu·Sep 6, 2024SaveLearn
Demkov-Fradkin tensor for curved harmonic oscillatorsIn this work, we obtain the Demkov-Fradkin tensor of symmetries for the quantum curved harmonic oscillator in a space with constant curvature given by a parameter . In order to construct this…Şengül Kuru, Javier Negro, Sergio Salamanca·Sep 5, 2024SaveLearn
The loop equations for noncommutative geometries on quiversWe define a path integral over Dirac operators that averages over noncommutative geometries on a fixed graph, as the title reveals, using quiver representations. We prove algebraic relations that are…Carlos Perez-Sanchez·Sep 5, 2024SaveLearn
Quantum optimal transport with convex regularizationThe goal of this paper is to settle the study of non-commutative optimal transport problems with convex regularization, in their static and finite-dimensional formulations. We consider both the…Emanuele Caputo, Augusto Gerolin, Nataliia Monina et al.·Sep 5, 2024SaveLearn
Spectral properties of hexagonal lattices with the -R couplingWe analyze the spectrum of the hexagonal lattice graph with a vertex coupling which manifestly violates the time reversal invariance and at high energies it asymptotically decouples edges at even…Pavel Exner, Jan Pekař·Sep 5, 2024SaveLearn
Propagators in curved spacetimes from operator theoryWe discuss two distinct operator-theoretic settings useful for describing (or defining) propagators associated with a scalar Klein-Gordon field on a Lorentzian manifold M. Typically, we assume that…Jan Dereziński, Christian Gaß·Sep 5, 2024SaveLearn
An elementary construction of the GKSL master equation for N-level systemsThe GKSL master equation for N-level systems provides a necessary and sufficient form for the generator of a quantum dynamical semigroup in the Schrodinger picture where the underlying Hilbert space…Matthew Ziemke·Sep 5, 2024SaveLearn
Mathematical ideas and notions of quantum field theoryThese are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT. The latest version (405 pages) is https://math.mit.edu/~etingof/gsm254.pdf (AMS…Pavel Etingof·Sep 4, 2024SaveLearn
SUSY Quantum Mechanics, (non)-Analyticity and … Phase TransitionsIt is shown by analyzing the 1D Schr\"odinger equation that discontinuities in the coupling constant can occur in both the energies and the eigenfunctions. Surprisingly, those discontinuities,…Alexander V Turbiner·Sep 4, 2024SaveLearn
Inverse problems for quantum graph associated with square and hexagonal latticesWe solve inverse problems from the D-N map for the quantum graph on a finite domain in a square lattice and that on a hexagonal lattice, as well as inverse scattering problems from the S-matrix for a…K. Ando, E. Blåsten, P. Exner et al.·Sep 4, 2024SaveLearn
Adinkras and Pure SpinorsThe nilpotence variety for extended supersymmetric quantum mechanics is a cone over a quadric in projective space. The pure spinor correspondence, which relates the description of off-shell…Richard Eager, Simone Noja, Raphael Senghaas et al.·Sep 4, 2024SaveLearn