Higher Dimensional Fourier Quasicrystals from Lee-Yang VarietiesIn this paper, we construct Fourier quasicrystals with unit masses in arbitrary dimensions. This generalizes a one-dimensional construction of Kurasov and Sarnak. To do this, we employ a class of…Lior Alon, Mario Kummer, Pavel Kurasov et al.·Jul 15, 2024SaveLearn
From bordisms of three-manifolds to domain walls between topological ordersWe study a correspondence between spin three-manifolds and bosonic abelian topological orders. Let N be a spin three-manifold. We can define a (2+1)-dimensional topological order TON…Yu Leon Liu, Dalton A R Sakthivadivel·Jul 15, 2024SaveLearn
Derivation of the Gross-Pitaevskii Dynamics through Renormalized Excitation Number OperatorsWe revisit the time evolution of initially trapped Bose-Einstein condensates in the Gross-Pitaevskii regime. We show that the system continues to exhibit BEC once the trap has been released and that…Christian Brennecke, Wilhelm Kroschinsky·Jul 15, 2024SaveLearn
Configuration Spaces of Points: A User's GuideThis user's guide (updated version) consists of two parts. The first part is an extensive survey contributed to the Encyclopedia of Mathematical Physics, 2nd edition. It covers many of the main…Sadok Kallel·Jul 14, 2024SaveLearn
Surprising symmetry properties and exact solutions of Kolmogorov backward equations with power diffusivityUsing the original advanced version of the direct method, we efficiently compute the equivalence groupoids and equivalence groups of two peculiar classes of Kolmogorov backward equations with power…Serhii D. Koval, Elsa Dos Santos Cardoso-Bihlo, Roman O. Popovych·Jul 14, 2024SaveLearn
General solution to Euler-Poisson equations of a free symmetric body by direct summation of power seriesEuler-Poisson equations describe the temporal evolution of a rigid body's orientation through the rotation matrix and angular velocity components, governed by first-order differential equations.…Guilherme Corrêa Silva·Jul 14, 2024SaveLearn
The Steklov problem for exterior domains: asymptotic behavior and applicationsWe investigate the spectral properties of the Steklov problem for the modified Helmholtz equation (p-) u = 0 in the exterior of a compact set, for which the positive parameter p ensures…Denis S. Grebenkov, Adrien Chaigneau·Jul 13, 2024SaveLearn
Exact local distribution of the absolutely continuous spectral measureIt is well-established that the spectral measure for one-frequency Schr\"odinger operators with Diophantine frequencies exhibits optimal 1/2-H\"older continuity within the absolutely continuous…Xianzhe Li, Jiangong You, Qi Zhou·Jul 12, 2024SaveLearn
Mean eigenvector self-overlap in deformed complex Ginibre ensembleConsider a random matrix of size N as an additive deformation of the complex Ginibre ensemble under a deterministic matrix X0 with a finite rank, independent of N. We prove that microscopic…Lu Zhang·Jul 12, 2024SaveLearn
On the Problem of Defining Charge Operators for the Dirac Quantum FieldIt is well known how to define the operator Q for the total charge (i.e., positron number minus electron number) on the standard Hilbert space of the second-quantized Dirac equation. Here we ask…Pablo Costa Rico, Roderich Tumulka·Jul 12, 2024SaveLearn
Quantum inverse scattering for the 20-vertex model up to Dynkin automorphism: 3D Poisson structure, triangular height functions, weak integrabilityWe initiate a novel application of the quantum inverse scattering method for the 20-vertex model, building upon seminal work from Faddeev and Takhtajan on the study of Hamiltonian systems. In…Pete Rigas·Jul 12, 2024SaveLearn
Coupling and Recoupling Coefficients for Wigner's U(4) Supermultiplet SymmetryA novel procedure for evaluating Wigner coupling coefficients and Racah recoupling coefficients for U(4) in two group-subgroup chains is presented. The canonical U(4)->U(3)->U(2)->U(1) coupling and…Phong Dang, Jerry P. Draayer, Feng Pan et al.·Jul 12, 2024SaveLearn
Conformal field theory of Gaussian free fields in a multiply connected domainWe implement a version of conformal field theory (CFT) that gives a connection to SLE in a multiply connected domain. Our approach is based on the Gaussian free field and applies to CFTs with central…Tom Alberts, Sung-Soo Byun, Nam-Gyu Kang·Jul 11, 2024SaveLearn
Scaling limit of domino tilings on a pentagonal domainWe consider the six-vertex model at its free-fermion point with domain wall boundary conditions, which is equivalent to random domino tilings of the Aztec diamond. We compute the scaling limit of a…Filippo Colomo, Andrei G. Pronko·Jul 10, 2024SaveLearn
Hamiltonians for Quantum Systems with Contact InteractionsWe discuss the problem of constructing self-adjoint and lower bounded Hamiltonians for a system of n>2 non-relativistic quantum particles in dimension three with contact (or zero-range or δ)…Daniele Ferretti, Alessandro Teta·Jul 9, 2024SaveLearn
A matrix solution to any polygon equationIn this article, we construct matrices associated to Pachner n-12-n-12 moves for odd n and matrices associated to Pachner (n2-1)-n2 moves for even n.…Zheyan Wan·Jul 9, 2024SaveLearn
Acoustic axes conditions revisedThe explanation of the basic acoustic properties of crystals requires a recognition of the acoustic axes. To derive the acoustic axes in a given material, one requires both a workable method and the…Yakov Itin·Jul 9, 2024SaveLearn
Electrostatics on Branching ProcessesWe introduce a random probability measure on the profinite completion of the random tree of a branching process and introduce the canonical and grand canonical ensembles of random repelling particles…Christopher D. Sinclair·Jul 8, 2024SaveLearn
Hierarchy of coupled Burgers-like equations induced by conditional symmetriesIt is known that Q-conditional symmetries of the classical Burgers' equation express in terms of three functions satisfying a coupled system of Burgers-like equations. The search of conditional…M. Gorgone, F. Oliveri, E. Sgroi·Jul 8, 2024SaveLearn
Dirac cones and magic angles in the Bistritzer--MacDonald TBG HamiltonianWe demonstrate the generic existence of Dirac cones in the full Bistritzer--MacDonald Hamiltonian for twisted bilayer graphene. Its complementary set, when Dirac cones are absent, is the set of magic…Simon Becker, Solomon Quinn, Zhongkai Tao et al.·Jul 8, 2024SaveLearn
Four no-go theorems on the existence of spin and orbital angular momentum of massless bosonsThe past decades have seen substantial interest in the so-called orbital angular momentum (OAM) of light, driven largely by its diverse range of applications. However, there are fundamental…Eric Palmerduca, Hong Qin·Jul 8, 2024SaveLearn
Pressure of a dilute spin-polarized Fermi gas: Upper boundWe prove an upper bound on the pressure of a dilute fully spin-polarized Fermi gas capturing the leading correction to the pressure of a free gas resulting from repulsive interactions. This…Asbjørn Bækgaard Lauritsen, Robert Seiringer·Jul 8, 2024SaveLearn
Global realisation of magnetic fields as 112D Hamiltonian systemsThe paper reviews the notion of n+12D non-autonomous Hamiltonian systems, portraying their dynamics as the flow of the Reeb field related to a closed two-form of maximal rank on a…Nathan Duignan, David Perrella, David Pfefferlé·Jul 8, 2024SaveLearn
Computation of -functions on plane algebraic curvesNumerical tools for computation of -functions, also known as Kleinian, or multiply periodic, are proposed. In this connection, computation of periods of the both first and second kinds is…Julia Bernatska·Jul 8, 2024SaveLearn
Monotonicity of the set of zeros of the Lyapunov exponent with respect to shift embeddingsWe consider the discrete Schr\"odinger operators with potentials whose values are read along the orbits of a shift of finite type. We study a certain subset of the collection of energies at which the…Oleg Safronov·Jul 7, 2024SaveLearn