Cartan Connections and Integrable Vortex EquationsWe demonstrate that integrable abelian vortex equations on constant curvature Riemann surfaces can be reinterpreted as flat non-abelian Cartan connections. By lifting to three dimensional group…Calum Ross·Dec 15, 2021SaveLearn
Factorizable Lie bialgebras, quadratic Rota-Baxter Lie algebras and Rota-Baxter Lie bialgebrasIn this paper, first we introduce the notion of quadratic Rota-Baxter Lie algebras of arbitrary weight, and show that there is a one-to-one correspondence between factorizable Lie bialgebras and…Honglei Lang, Yunhe Sheng·Dec 15, 2021SaveLearn
The Hamilton-Jacobi analysis for higher-order Chern-Simons gravityThe Hamilton-Jacobi [HJ] analysis for higher-order Chern-Simons gravity is performed. The complete set of HJ Hamiltonians are identified and a fundamental HJ differential is constructed, from…Alberto Escalante, J. Aldair Pantoja-Gonzalez, D. Vanessa Castro-Luna·Dec 14, 2021SaveLearn
Revisiting the Coulomb problem: A novel representation of the confluent hypergeometric function as an infinite sum of discrete Bessel functionsWe use the tridiagonal representation approach to solve the radial Schrödinger equation for the continuum scattering states of the Coulomb problem in a complete basis set of discrete Bessel…A. D. Alhaidari·Dec 14, 2021SaveLearn
Quantitatively improved finite-size criteria for spectral gapsFinite-size criteria have emerged as an effective tool for deriving spectral gaps in higher-dimensional frustration-free quantum spin systems. We quantitatively improve the existing finite-size…Marius Lemm, David Xiang·Dec 14, 2021SaveLearn
The Virasoro-like Algebra of a Frobenius ManifoldFor an arbitrary calibrated Frobenius manifold, we construct an infinite dimensional Lie algebra, called the Virasoro-like algebra, which is a deformation of the Virasoro algebra of the Frobenius…Si-Qi Liu, Di Yang, Youjin Zhang et al.·Dec 14, 2021SaveLearn
Scattering matrix of elementary excitations in the antiperiodic XXZ spin chain with η=iπ/3We study the thermodynamic limit of the antiperiodic XXZ spin chain with the anisotropic parameter η=πi3. We parameterize eigenvalues of the transfer matrix by their zero points instead of…Pei Sun, Jintao Yang, Yi Qiao et al.·Dec 14, 2021SaveLearn
The Dry Ten Martini Problem at CriticalityWe apply recently developed methods for the construction of quasi-periodic transfer matrices to the Dry Ten Martini problem for the critical almost-Mathieu Operator, also known as the…Dan S. Borgnia, Robert-Jan Slager·Dec 13, 2021SaveLearn
Minimal twist of almost commutative geometriesWe classify the twists of almost commutative spectral triples that keep the Hilbert space and the Dirac operator untouched. The involved twisting operator is shown to be the product of the grading of…Manuele Filaci, Pierre Martinetti·Dec 12, 2021SaveLearn
Transformations, symmetries and Noether theorems for differential-difference equationsThe first part of this paper develops a geometric setting for differential-difference equations that resolves an open question about the extent to which continuous symmetries can depend on discrete…Linyu Peng, Peter E Hydon·Dec 11, 2021SaveLearn
Soliton shielding of the focusing Nonlinear Schrödinger EquationWe first consider a deterministic gas of N solitons for the Focusing Nonlinear Schrödinger (FNLS) equation in the limit N∞ with a point spectrum chosen to interpolate a given spectral…Marco Bertola, Tamara Grava, Giuseppe Orsatti·Dec 11, 2021SaveLearn
Multistability for a Reduced Nematic Liquid Crystal Model in the Exterior of 2D PolygonsWe study nematic equilibria in an unbounded domain, with a two-dimensional regular polygonal hole with K edges, in a reduced Landau-de Gennes framework. This complements our previous work on the…Yucen Han, Apala Majumdar·Dec 10, 2021SaveLearn
Geometry of inhomogeneous Poisson brackets, multicomponent Harry Dym hierarchies and multicomponent Hunter-Saxton equationsWe introduce a natural class of multicomponent local Poisson structures Pk + P1, where P1 is a local Poisson bracket of order one and Pk is a homogeneous…Andrey Yu. Konyaev·Dec 10, 2021SaveLearn
Non-linear Schrodinger equation with time-dependent balanced loss-gain and space-time modulated non-linear interactionWe consider a class of one dimensional vector Non-linear Schrodinger Equation(NLSE) in an external complex potential with Balanced Loss-Gain(BLG) and Linear Coupling(LC) among the components…Supriyo Ghosh, Pijush K. Ghosh·Dec 9, 2021SaveLearn
Small Oscillations of a Vortex Ring: Hamiltonian Formalism and QuantizationThis article investigates small oscillations of a vortex ring with zero thickness that evolves under the Local Induction Equation (LIE). We deduce the differential equation that describes the…S. V. Talalov·Dec 9, 2021SaveLearn
A note on dependent random variables in quantum dynamicsWe consider the many-body time evolution of weakly interacting bosons in the mean field regime for initial coherent states. We show that bounded k-particle operators, corresponding to dependent…Simone Rademacher·Dec 9, 2021SaveLearn
How to Draw a Correlation FunctionWe discuss connection between the XX0 Heisenberg spin chain and some aspects of enumerative combinatorics. The representation of the Bethe wave functions via the Schur functions allows to apply the…Nikolay Bogoliubov, Cyril Malyshev·Dec 9, 2021SaveLearn
A geometric perspective on the scaling limits of critical Ising and φ4d modelsThe lecture delivered at the Current Developments in Mathematics conference (Harvard-MIT, 2021) focused on the recent proof of the Gaussian structure of the scaling limits of the critical…Michael Aizenman·Dec 8, 2021SaveLearn
The Lagrange-D'Alembert Principle in Banach SpaceThe Lagrange-D'Alembert Principle is one of the fundamental tools of classical mechanics. We generalize this principle to mechanics-like ODE in Banach spaces. As an application we discuss…Oleg Zubelevich·Dec 8, 2021SaveLearn
Finite-rank complex deformations of random band matrices: sigma-model approximationWe study the distribution of complex eigenvalues z1,…, zN of random Hermitian N× N block band matrices with a complex deformation of a finite rank. Assuming that the width of the band…Mariya Shcherbina, Tatyana Shcherbina·Dec 8, 2021SaveLearn
Covariant Star Product on Semi-Conformally Flat Noncommutative Calabi-Yau Manifolds and Noncommutative Topological Index TheoremA differential geometric version of noncommutative topological index theorem is worked out for covariant star products on noncommutative vector bundles. For start, a noncommutative manifold is…A. A. Varshovi·Dec 8, 2021SaveLearn
An approach to p-adic qubits from irreducible representations of SO(3)pWe introduce the notion of p-adic quantum bit (p-qubit) in the context of the p-adic quantum mechanics initiated and developed by Volovich and his followers. In this approach, physics takes…Ilaria Svampa, Stefano Mancini, Andreas Winter·Dec 6, 2021SaveLearn
Diffraction by a Right-Angled No-Contrast Penetrable Wedge Revisited: A Double Wiener-Hopf ApproachIn this paper, we revisit Radlow's innovative approach to diffraction by a penetra ble wedge by means of a double Wiener-Hopf technique. We provide a constructive way of obtaining his ansatz and…Valentin D. Kunz, Raphael C. Assier·Dec 6, 2021SaveLearn
Purely linear response of the quantum Hall current to space-adiabatic perturbationsUsing recently developed tools from space-adiabatic perturbation theory, in particular the construction of a non-equilibrium almost stationary state, we give a new proof that the Kubo formula for the…Giovanna Marcelli, Domenico Monaco·Dec 6, 2021SaveLearn
The Amplituhedron BCFW TriangulationThe amplituhedron Ank4 is a geometric object, introduced by Arkani-Hamed and Trnka (2013) in the study of scattering amplitudes in quantum field theories. They conjecture that Ank4 admits a…Chaim Even-Zohar, Tsviqa Lakrec, Ran J. Tessler·Dec 5, 2021SaveLearn