On Infinite Series of Bessel functions of the First Kind: Σ JN+p(x), Σ (-1) JN+p(x)Infinite series of Bessel function of the first kind, Σ∞ JN+p(x), Σ∞ (-1) JN+p(x), are summed in closed form. These expressions are evaluated…Suk Hyun Sung, Robert Hovden·Nov 1, 2022SaveLearn
SO(3)-Knot States and the Volume ConjectureWe study the alternating subspace of holomorphic sections of a special prequantum line bundle over SU(2)-character variety of torus, and show that it is isomorphic to the projective representation of…Honghuai Fang·Nov 1, 2022SaveLearn
On the Joint Evolution Problem for a Scalar Field and its SingularityIn the classical electrodynamics of point charges in vacuum, the electromagnetic field, and therefore the Lorentz force, is ill-defined at the locations of the charges. Kiessling resolved this…Aditya Agashe, Ethan Lee, A. Shadi Tahvildar-Zadeh·Nov 1, 2022SaveLearn
Quantum Groups, Discrete Magnus Expansion, Pre-Lie and Tridendriform AlgebrasWe review the discrete evolution problem and the corresponding solution as a discrete Dyson series in order to rigorously derive a generalized discrete version of the Magnus expansion. We also…Anastasia Doikou·Nov 1, 2022SaveLearn
Classical limit of Gibbs states for quantum spin systemsWe study the relation between quantum mechanical and classical Gibbs states of spin systems with spin quantum number s. It is known that quantum states and observables can be represented by…Heinz-Jürgen Schmidt·Nov 1, 2022SaveLearn
Absence of submultiplicative norms for Wick-ordered Operator ProductsIn this paper, a key problem of the rigorous formulation of the renormalization group as a continuous flow is identified. Some essential features of the operator-theoretic renormalization group are…Jakob Geisler·Nov 1, 2022SaveLearn
Recurrence relations and general solution of the exceptional Hermite equationExceptional orthogonal Hermite and Laguerre polynomials have been linked to the k-step extension of harmonic and singular oscillators. The exceptional polynomials allow the existence of different…Alfred Michel Grundland, Danilo Latini, Ian Marquette·Nov 1, 2022SaveLearn
Extreme eigenvalues and the emerging outlier in rank-one non-Hermitian deformations of the Gaussian Unitary EnsembleComplex eigenvalues of random matrices J=GUE + iγ (1, 0, …, 0) provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a…Yan V. Fyodorov, Boris A. Khoruzhenko, Mihail Poplavskyi·Oct 31, 2022SaveLearn
Analytic continuations of the Horn H1 and H5 functionsThe analytic continuations (ACs) of the double variable Horn H1 and H5 functions have been derived for the first time using the automated symbolic Mathematica package…Souvik Bera, Tanay Pathak·Oct 31, 2022SaveLearn
Absence of excited eigenvalues for Fr\"ohlich type polaron models at weak couplingWe consider a class of polaron models, including the Fr\"ohlich model, at zero total momentum, and show that at sufficiently weak coupling there are no excited eigenvalues below the essential…Robert Seiringer·Oct 31, 2022SaveLearn
Superintegrable quantum mechanical systems with position dependent masses invariant with respect to three parametric Lie groupsQuantum mechanical systems with position dependent masses (PDM) admitting for and more dimensional symmetry algebras are classified. Namely, all PDM systems are specified which, in addition to their…A. G. Nikitin·Oct 30, 2022SaveLearn
Degenerate perturbation theory for models of quantum field theory with symmetriesWe consider Hamiltonians of models describing non-relativistic quantum mechanical matter coupled to a relativistic field of bosons. If the free Hamiltonian has an eigenvalue, we show that this…David Hasler, Markus Lange·Oct 30, 2022SaveLearn
Construction of Global Solutions to the Linearized Field Equations for Causal Variational PrinciplesWe give a novel construction of global solutions to the linearized field equations for causal variational principles. The method is to glue together local solutions supported in lens-shaped regions.…Felix Finster, Margarita Kraus·Oct 29, 2022SaveLearn
Energetic variational approaches for multiphase flow systems with phase transitionWe study the governing equations for the motion of the fluid particles near air-water interface from an energetic point of view. Since evaporation and condensation phenomena occur at the interface,…Hajime Koba·Oct 29, 2022SaveLearn
Quantum Systems at The BrinkWe present a method to calculate the asymptotic behavior of eigenfunctions of Schr\"odinger operators that also works at the threshold of the essential spectrum. It can be viewed as a higher order…Dirk Hundertmark, Michal Jex, Markus Lange·Oct 28, 2022SaveLearn
Shape reconstructions by using plasmon resonances with enhanced sensitivityThis paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously…M. H. Ding, H. Y. Liu, G. H. Zheng·Oct 28, 2022SaveLearn
OPEs of rank two W-algebrasIn this short note, we provide OPEs for several affine W-algebras associated with Lie algebras of rank two and give some direct applications.Justine Fasquel·Oct 27, 2022SaveLearn
The Adiabatic Wigner-Weisskopf ModelWe consider a slowly varying time dependent d-level atom interacting with a photon field. Restricted to the single excitation atom-field sector, the model is a time-dependent generalization of the…Alain Joye, Marco Merkli·Oct 27, 2022SaveLearn
Renormalization of spinx2013boson interactions mediated by singular form factorsWe study and discuss the extension of the rotating-wave spinx2013boson model, together with more general models describing a systemx2013field coupling with a similar…Davide Lonigro·Oct 27, 2022SaveLearn
Towards bosonization of Virasoro coadjoint orbitsWe show that Schwarzian theories associated to certain hyperbolic and parabolic Virasoro coadjoint orbits admit bosonization, i.e. a global S1-equivariant Darboux chart in which the corresponding…Anton Alekseev, Olga Chekeres, Donald R. Youmans·Oct 27, 2022SaveLearn
Non-trivial bundles and Algebraic Classical Field TheoryInspired by the recent algebraic approach to classical field theory, we propose a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is the notion of…Romeo Brunetti, Andrea Moro·Oct 26, 2022SaveLearn
Localization in the random XXZ quantum spin chainWe study the many-body localization (MBL) properties of the Heisenberg XXZ spin-12 chain in a random magnetic field. We prove that the system exhibits localization in any given energy interval…Alexander Elgart, Abel Klein·Oct 26, 2022SaveLearn
Sharp inequalities for coherent states and their optimizersWe are interested in sharp functional inequalities for the coherent state transform related to the Wehrl conjecture and its generalizations. This conjecture was settled by Lieb in the case of the…Rupert L. Frank·Oct 26, 2022SaveLearn
Time evolution and the Schr\"odinger equation on time dependent quantum graphsThe purpose of the present paper is to discuss the time dependent Schr\"odinger equation on a metric graph with time-dependent edge lengths, and the proper way to pose the problem so that the…Uzy Smilansky, Gilad Sofer·Oct 26, 2022SaveLearn
Classification of degenerate non-homogeneous Hamiltonian operatorsIn this paper, the authors investigate non-homogeneous Hamiltonian operators composed of a first-order Dubrovin-Novikov operator and an ultralocal one. The study of such operators turns out to be…Marta Dell'Atti, Pierandrea Vergallo·Oct 25, 2022SaveLearn