Feynman path integrals on compact Lie groups with bi-invariant Riemannian metricsIn this work we consider a suitable generalization of the Feynman path integral on a specific class of Riemannian manifolds consisting of compact Lie groups with bi-invariant Riemannian metrics. The…Nicoló Drago, Sonia Mazzucchi, Valter Moretti·Jul 6, 2023SaveLearn
Arctic curves of the four-vertex modelWe consider the four-vertex model with a special choice of fixed boundary conditions giving rise to limit shape phenomena. More generally, the considered boundary conditions relate vertex models to…I. N. Burenev, F. Colomo, A. Maroncelli et al.·Jul 6, 2023SaveLearn
Joint moments of higher order derivatives of CUE characteristic polynomials II: Structures, recursive relations, and applicationsIn a companion paper jon-fei, we established asymptotic formulae for the joint moments of derivatives of the characteristic polynomials of CUE random matrices. The leading order coefficients…Jonathan P. Keating, Fei Wei·Jul 6, 2023SaveLearn
Infinite affine, hyperbolic and Lorentzian Weyl groups with their associated Calogero modelsWe propose generalizations of Calogero models that exhibit invariance with respect to the infinite Weyl groups of affine, hyperbolic, and Lorentzian types. Our approach involves deriving closed…Francisco Correa, Andreas Fring, Octavio Quintana·Jul 5, 2023SaveLearn
The phase transition for the three-state SOS model with one-level competing interactions on the binary treeIn this paper, we consider a three-state solid-on-solid (SOS) model with two competing interactions (nearest-neighbour, one-level next-nearest-neighbour) on the Cayley tree of order two. We show that…Muzaffar M. Rahmatullaev, Obid Sh. Karshiboev·Jul 5, 2023SaveLearn
Vacuum polarisation without infinitiesIn honour of Detlef D\"urr, we report on a mathematical rigorous computation of the electric vacuum polarisation current and extract the well-known expression for the second order perturbation.…Dirk - André Deckert, Franz Merkl, Markus Nöth·Jul 5, 2023SaveLearn
Non-perturbative solutions of hierarchies of evolution equations for colliding particlesThe article deals with the challenge of the construction of solutions to hierarchies of fundamental evolution equations for many colliding particles. The method of cluster expansions of the groups of…V. I. Gerasimenko, I. V. Gapyak·Jul 5, 2023SaveLearn
Deformation and quantisation condition of the Q-top recursionWe consider a deformation of a family of hyperelliptic refined spectral curves and investigate how deformation effects appear in the hyperelliptic refined topological recursion as well as the…Kento Osuga·Jul 5, 2023SaveLearn
Logarithmically enhanced area-laws for fermions in vanishing magnetic fields in dimension twoWe consider fermionic ground states of the Landau Hamiltonian, HB, in a constant magnetic field of strength B>0 in R2 at some fixed Fermi energy μ>0, described by the Fermi…Paul Pfeiffer, Wolfgang Spitzer·Jul 4, 2023SaveLearn
Joint moments of higher order derivatives of CUE characteristic polynomials I: asymptotic formulaeWe derive explicit asymptotic formulae for the joint moments of the n1-th and n2-th derivatives of the characteristic polynomials of CUE random matrices for any non-negative integers $n1,…Jonathan P. Keating, Fei Wei·Jul 4, 2023SaveLearn
Dynamical Localization for the Singular Anderson Model in ZdWe prove that once one has the ingredients of a ``single-energy multiscale analysis (MSA) result'' on the Zd lattice, several spectral and dynamical localization results can be derived,…Nishant Rangamani, Xiaowen Zhu·Jul 4, 2023SaveLearn
Duality of O(N) and Sp(N) random tensor models: tensors with symmetriesIn a recent series of papers, a duality between orthogonal and symplectic random tensor models has been proven, first for quartic models and then for models with interactions of arbitrary order.…H. Keppler, T. Krajewski, T. Muller et al.·Jul 4, 2023SaveLearn
Pressure of a dilute spin-polarized Fermi gas: Lower boundWe consider a dilute spin-polarized Fermi gas at positive temperature in dimensions d∈\1,2,3\. We show that the pressure of the interacting gas is bounded from below by that of the free gas…Asbjørn Bækgaard Lauritsen, Robert Seiringer·Jul 3, 2023SaveLearn
Dyson-Schwinger equations in zero dimensions and polynomial approximationsThe Dyson-Schwinger (DS) equations for a quantum field theory in D-dimensional space-time are an infinite sequence of coupled integro-differential equations that are satisfied exactly by the…Carl M. Bender, Christos Karapoulitidis, S. P. Klevansky·Jul 3, 2023SaveLearn
Focusing dynamics of 2D Bose gases in the instability regimeWe consider the dynamics of a 2D Bose gas with an interaction potential of the form N2β-1w(Nβ·) for β∈ (0,3/2). The interaction may be chosen to be negative and large,…Lea Boßmann, Charlotte Dietze, Phan Thành Nam·Jul 3, 2023SaveLearn
Dual formulation for constraint solutions of the multi-state Choquard equationThe Choquard equation is a partial differential equation that has gained significant interest and attention in recent decades. It is a nonlinear equation that combines elements of both the Laplace…Gershon Wolansky·Jul 3, 2023SaveLearn
Positive mass gap of quantum Yang-Mills FieldsWe construct a 4-dimensional quantum field theory on a Hilbert space, dependent on a simple Lie Algebra of a compact Lie group, that satisfies Wightman's axioms. This Hilbert space can be written as…Adrian P. C. Lim·Jul 3, 2023SaveLearn
Evaluation of the second virial coefficient for the Mie potential using the method of bracketsThe second virial coefficient for the Mie potential is evaluated using the method of brackets. This method converts a definite integral into a series in the parameters of the problem, in this case…Ivan Gonzalez, Igor Kondrashuk, Victor H. Moll et al.·Jul 2, 2023SaveLearn
On the role of the Integrable Toda model in one-dimensional molecular dynamicsWe prove that the common Mie-Lennard-Jones (MLJ) molecular potentials, appropriately normalized via an affine transformation, converge, in the limit of hard-core repulsion, to the Toda exponential…Giancarlo Benettin, Giuseppe Orsatti, Antonio Ponno·Jul 2, 2023SaveLearn
Multichannel scattering for the Schr\"odinger equation on a line with different thresholds at both infinitiesThe multichannel scattering problem for the stationary Schr\"odinger equation on a line with different thresholds at both infinities is investigated. The analytical structure of the Jost solutions…P. O. Kazinski, P. S. Korolev·Jul 2, 2023SaveLearn
Microcanonical phase transitions for the vortex systemWe consider the Microcanonical Variational Principle for the vortex system in a bounded domain. In particular we are interested in the thermodynamic properties of the system in domains of second…Dario Benedetto, Emanuele Caglioti, Margherita Nolasco·Jul 1, 2023SaveLearn
Upper bounds for the number of isolated critical points via Thom-Milnor theoremWe apply the Thom-Milnor theorem to obtain the upper bounds on the amount of isolated (1) critical points of a potential generated by several fixed point charges(Maxwell's problem on point charges),…Vladimir Zolotov·Jul 1, 2023SaveLearn
3D Boson representation of affine Yangian of gl(1) and 3D cut-and-join operatorsWe have constructed 3D Bosons. In this paper, we show the 3D Bosonic Fock space, which is isomorphic to the vector space of 3D Young diagrams as graded vector spaces. We use 3D Bosons to represent…Na Wang, Can Zhang, Ke Wu·Jun 30, 2023SaveLearn
Perturbative QFT: off-shell fields, deformation quantization and causal perturbation theoryPerturbative QFT is developed in terms of off-shell fields (that is, functionals on the configuration space not restricted by any field equation), and by quantizing the (underlying) free theory by an…Michael Duetsch·Jun 30, 2023SaveLearn
Stabilization against collapse of 2D attractive Bose-Einstein condensates with repulsive, three-body interactionsWe consider a trapped Bose gas of N identical bosons in two dimensional space with both an attractive, two-body, scaled interaction and a repulsive, three-body, scaled interaction respectively of…Dinh-Thi Nguyen, Julien Ricaud·Jun 30, 2023SaveLearn