The Pirogov-Sinai Theory for Infinite InteractionsThe purpose of this note is to consider a number of straightforward generalizations of the Pirogov-Sinai theory which can be covered by minor additions to the canonical texts. These generalizations…A. Mazel, I. Stuhl, Y. Suhov·Sep 3, 2024SaveLearn
Limiting eigenvalue distribution of the general deformed Ginibre ensembleConsider the n× n matrix Xn=An+Hn, where An is a n× n matrix (either deterministic or random) and Hn is a n× n matrix independent from An drawn from complex Ginibre…Roman Sarapin·Sep 3, 2024SaveLearn
Moments of characteristic polynomials and their derivatives for SO(2N) and USp(2N) and their application to one-level density in families of elliptic curve L-functionsUsing the ratios theorems, we calculate the leading order terms in N for the following averages of the characteristic polynomial and its derivative: $< |A(1 )| r …I. A. Cooper, N. C. Snaith·Sep 3, 2024SaveLearn
An integrable pseudospherical equation with pseudo-peakon solutionsWe study an integrable equation whose solutions define a triad of one-forms describing a surface with Gaussian curvature -1. We identify a local group of diffeomorphisms that preserve these solutions…Priscila Leal da Silva, Igor Leite Freire, Nazime Sales Filho·Sep 3, 2024SaveLearn
Newell-Whitehead-Segel Equation: An Exact, Generalized SolutionDerivation of an exact, general solution to Newell-Whitehead-Segel transient, nonlinear partial differential equation is provided for one to three dimensional cases, also, arbitrary power of…Luisiana Cundin·Sep 2, 2024SaveLearn
Lieb-Thirring inequalities for the shifted Coulomb HamiltonianIn this paper we prove sharp Lieb-Thirring (LT) inequalities for the family of shifted Coulomb Hamiltonians. More precisely, we prove the classical LT inequalities with the semi-classical constant…Thiago Carvalho Corso, Timo Weidl, Zhuoyao Zeng·Sep 2, 2024SaveLearn
Error exponents for entanglement transformations from degenerationsThis paper explores the trade-off relation between the rate and the strong converse exponent for asymptotic LOCC transformations between pure multipartite states. Any single-copy probabilistic…Dávid Bugár, Péter Vrana·Sep 2, 2024SaveLearn
Classification of symmetry protected states of quantum spin chains for continuous symmetry groupsSymmetry protected states (SPT's) of quantum spin systems were studied by several authors. For one-dimensional systems (spin chains), there is an essentially complete and rigorous understanding:…Bruno de Oliveira Carvalho, Wojciech De Roeck, Tijl Jappens·Sep 2, 2024SaveLearn
Ensemble inter-relations in random matrix theoryThe ensemble inter-relations to be considered are special features of classical cases, where the joint eigenvalue probability density can be computed explicitly. Attention will be focussed too on the…Peter J. Forrester·Sep 2, 2024SaveLearn
How a Space-Time Singularity Helps Remove the Ultraviolet Divergence ProblemParticle creation terms in quantum Hamiltonians are usually ultraviolet divergent and thus mathematically ill defined. A rather novel way of solving this problem is based on imposing so-called…Joscha Henheik, Bipul Poudyal, Roderich Tumulka·Sep 1, 2024SaveLearn
Bounds on Tc in the Eliashberg theory of Superconductivity. I: The γ-modelUsing the recent reformulation for the Eliashberg theory of superconductivity in terms of a classical interacting Bloch spin chain model, rigorous upper and lower bounds on the critical temperature…Michael K. -H. Kiessling, Boris L. Altshuler, Emil A. Yuzbashyan·Aug 31, 2024SaveLearn
Bounds on Tc in the Eliashberg theory of Superconductivity. II: Dispersive phononsThe standard Eliashberg theory of superconductivity is studied, in which the effective electron-electron interactions are mediated by generally dispersive phonons, with Eliashberg spectral function…Michael K. -H. Kiessling, Boris L. Altshuler, Emil A. Yuzbashyan·Aug 31, 2024SaveLearn
2D attractive almost-bosonic anyon gasesIn two-dimensional space, we consider a system of N anyons interacts via a short range attractive two-body interaction. In the stable regime, we derive the average-field Pauli functional as the…Dinh-Thi Nguyen·Aug 31, 2024SaveLearn
Relativistic Exchange BoundsWe collect estimates of the exchange energy of the relativistic no-pair Hartree-Fock and M\"uller functional and use them to show the existence of a minimizer and stability of matter of the…Long Meng, Heinz Siedentop, Matthias Tiefenbeck·Aug 30, 2024SaveLearn
Long time quantum-classical correspondence for open systems in trace normWe consider a frictionless system coupled to an external Markovian environment. The quantum and classical evolution of such systems are described by the Lindblad and the Fokker-Planck equation…Zhenhao Li·Aug 30, 2024SaveLearn
Algebraic method of group classification for semi-normalized classes of differential equationsWe generalize the notion of semi-normalized classes of systems of differential equations, study properties of such classes and extend the algebraic method of group classification to them. In…Celestin Kurujyibwami, Dmytro R. Popovych, Roman O. Popovych·Aug 29, 2024SaveLearn
Invariants of the quantum graph of the partial traceWe compute the independence number, zero-error capacity, and the values of the Lov\'asz function and the quantum Lov\'asz function for the quantum graph associated to the partial trace quantum…Wojciech Paupa, Piotr M. Sołtan·Aug 29, 2024SaveLearn
Small deviations of Gaussian multiplicative chaos and the free energy of the two-dimensional massless Sinh--Gordon modelWe prove a global decomposition result for -correlated Gaussian fields on the d-dimensional torus and use this to derive new small deviations bounds for a class of Gaussian multiplicative…Nikolay Barashkov, Joona Oikarinen, Mo Dick Wong·Aug 29, 2024SaveLearn
Two-dimensional Fireballs as a Lagrangian Ermakov SystemThe equations of motion for the variance of strictly one-dimensional or two-dimensional non-relativistic fireballs are derived, from the hydrodynamic equations for an ideal, structureless Boltzmann…Fernando Haas·Aug 29, 2024SaveLearn
H\"older continuity of the integrated density of states for Liouville frequenciesWe prove H\"older continuity of the Lyapunov exponent L(ω,E) and the integrated density of states at energies that satisfy L(ω,E)>4(ω,E)· β(ω)≥ 0 for general…Rui Han, Wilhelm Schlag·Aug 28, 2024SaveLearn
Tree-tubings and the combinatorics of resurgent Dyson-Schwinger equationsWe give a novel combinatorial interpretation to the perturbative series solutions for a class of Dyson-Schwinger equations. We show how binary tubings of rooted trees with labels from an alphabet on…Michael Borinsky, Gerald V. Dunne, Karen Yeats·Aug 28, 2024SaveLearn
Hessian spectrum at the global minimum of the spherical pure-like mixed p-spin glassesWe study the large N-dimensional limit of the Hessian spectrum at the global minimum of some subclasses of the spherical mixed p-spin models. Specifically, we show that its empirical spectral…Hao Xu, Haoran Yang·Aug 28, 2024SaveLearn
Causal perturbative QED and white noiseWe present the Bogoliubov's causal perturbative QFT, which includes only one refinement: the creation-annihilation operators at a point, i.e. for a specific momentum, are mathematically…Jaroslaw Wawrzycki·Aug 28, 2024SaveLearn
Power spectra of Dyson's circular ensemblesThe power spectrum is a Fourier series statistic associated with the covariances of the displacement from average positions of the members of an eigen-sequence. When this eigen-sequence has…Peter J. Forrester, Nicholas S. Witte·Aug 28, 2024SaveLearn
Relative Equilibria for Scaling Symmetries and Central ConfigurationsIn this paper, we explore scaling symmetries within the framework of symplectic geometry. We focus on the action of the multiplicative group G = R+ on exact symplectic manifolds…Giovanni Rastelli, Manuele Santoprete·Aug 27, 2024SaveLearn