Dunkl and Cherednik operatorsThis survey article, written for the Encyclopedia of Mathematical Physics, 2nd edition, is devoted to the remarkable family of operators introduced by Charles Dunkl and to their q-analogues…Oleg Chalykh·Sep 13, 2024SaveLearn
Proof of the Landau-Pekar Formula for the effective Mass of the Polaron at strong couplingWe study the Fr\"ohlich polaron in the regime of strong coupling and prove the asymptotically sharp lower bound on the effective mass $meff(α)≥ α4…Morris Brooks·Sep 13, 2024SaveLearn
Ground state energy is not always convex in the number of electronsWe provide the first counterexample showing that the ground state energy of electrons in an external Coulomb potential is not always a convex function of the number of electrons. This convexity has…Simone Di Marino, Mathieu Lewin, Luca Nenna·Sep 13, 2024SaveLearn
Non-unitary Wightman CFTs and non-unitary vertex algebrasWe give an equivalence of categories between: (i) M\"obius vertex algebras which are equipped with a choice of generating family of quasiprimary vectors, and (ii) (not-necessarily-unitary)…Sebastiano Carpi, Christopher Raymond, Yoh Tanimoto et al.·Sep 13, 2024SaveLearn
Unitary and Open Scattering Quantum Walks on GraphsWe study a class of Unitary Quantum Walks on arbitrary graphs, parameterized by a family of scattering matrices. These Scattering Quantum Walks model the discrete dynamics of a system on the edges of…Alain Joye·Sep 12, 2024SaveLearn
Delay ordinary differential equations: from Lagrangian approach to Hamiltonian approachThe paper suggests a Hamiltonian formulation for delay ordinary differential equations (DODEs). Such equations are related to DODEs with a Lagrangian formulation via a delay analog of the Legendre…Vladimir Dorodnitsyn, Roman Kozlov, Sergey Meleshko·Sep 12, 2024SaveLearn
Affine generalizations of the nonholonomic problem of a convex body rolling without slipping on the planeWe introduce a class of examples which provide an affine generalization of the nonholonomic problem of a convex body rolling without slipping on the plane. We investigate dynamical aspects of the…M. Costa Villegas, L. C. García-Naranjo·Sep 12, 2024SaveLearn
ODE/IM correspondence in the semiclassical limit: Large degree asymptotics of the spectral determinants for the ground state potentialWe study a Schr\"odinger-like equation for the anharmonic potential x2 α+(+1) x-2-E when the anharmonicity α goes to +∞. When E and vary in bounded…Gabriele Degano·Sep 12, 2024SaveLearn
Relative Dynamics of Vortices in Confined Bose--Einstein CondensatesWe consider the relative dynamics -- the dynamics modulo rotational symmetry in this particular context -- of N vortices in confined Bose--Einstein Condensates (BEC) using a finite-dimensional…Tomoki Ohsawa·Sep 11, 2024SaveLearn
Bootstrapping the critical behavior of multi-matrix modelsGiven a matrix model, by combining the Schwinger-Dyson equations with positivity constraints on its solutions, in the large N limit one is able to obtain explicit and numerical bounds on its…Masoud Khalkhali, Nathan Pagliaroli, Andrei Parfeni et al.·Sep 11, 2024SaveLearn
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