Coloured combinatorial maps and quartic bi-tracial 2-matrix ensembles from noncommutative geometryWe compute the first twenty moments of three convergent quartic bi-tracial 2-matrix ensembles in the large N limit. These ensembles are toy models for Euclidean quantum gravity originally proposed…Masoud Khalkhali, Nathan Pagliaroli·Dec 16, 2023SaveLearn
Ultraviolet Renormalisation of a Quantum Field Toy Model IIWe consider a class of toy models describing a fermion field coupled with a boson field. The model can be viewed as a Yukawa model but with scalar fermions. As in our first paper, the interaction…Benjamin Alvarez, Jacob Schach Møller·Dec 16, 2023SaveLearn
Characteristic polynomials of sparse non-Hermitian random matricesWe consider the asymptotic local behavior of the second correlation function of the characteristic polynomials of sparse non-Hermitian random matrices Xn whose entries have the form…Ievgenii Afanasiev, Tatyana Shcherbina·Dec 15, 2023SaveLearn
Nonlinear and nonlocal models of heat conduction in continuum thermodynamicsThe aim of this paper is to develop a general constitutive scheme within continuum thermodynamics to describe the behavior of heat flow in deformable media. Starting from a classical thermodynamic…Claudio Giorgi, Federico Zullo·Dec 15, 2023SaveLearn
Weyl formula and thermodynamics of geometric flowWe study the Weyl formula for the asymptotic number of eigenvalues of the Laplace-Beltrami operator with Dirichlet boundary condition on a Riemannian manifold in the context of geometric flows.…Parikshit Dutta, Arghya Chattopadhyay·Dec 15, 2023SaveLearn
Semimartingale driven mechanics and reduction by symmetry for stochastic and dissipative dynamical systemsThe recent interest in structure preserving stochastic Lagrangian and Hamiltonian systems raises questions regarding how such models are to be understood and the principles through which they are to…Oliver D. Street, So Takao·Dec 15, 2023SaveLearn
Exponentially localised interface eigenmodes in finite chains of resonatorsThis paper studies wave localisation in chains of finitely many resonators. There is an extensive theory predicting the existence of localised modes induced by defects in infinitely periodic systems.…Habib Ammari, Silvio Barandun, Bryn Davies et al.·Dec 15, 2023SaveLearn
Wave Propagation in Pure-Time Modulated Step Media With Applications to Temporal-AimingWe analyze the propagation of an incident electromagnetic wave in a purely-time modulated medium. Precisely, we assume that the permeability is unchanged while the permittivity has a multiple-step…Mourad Sini, Haibing Wang, Qingyun Yao·Dec 15, 2023SaveLearn
Position-momentum conditioning, relative entropy decomposition and convergence to equilibrium in stochastic Hamiltonian systemsThis paper is concerned with a class of multivariable stochastic Hamiltonian systems whose generalised position is related by an ordinary differential equation to the momentum governed by an Ito…Igor G. Vladimirov·Dec 15, 2023SaveLearn
Physics-Informed Deep Learning of Rate-and-State Fault FrictionDirect observations of earthquake nucleation and propagation are few and yet the next decade will likely see an unprecedented increase in indirect, surface observations that must be integrated into…Cody Rucker, Brittany A. Erickson·Dec 14, 2023SaveLearn
A symplectic approach to Schr\"odinger equations in the infinite-dimensional unbounded settingBy using the theory of analytic vectors and manifolds modelled on normed spaces, we provide a rigorous symplectic differential geometric approach to t-dependent Schr\"odinger equations on separable…Javier de Lucas, Julia Lange, Xavier Rivas·Dec 14, 2023SaveLearn
Random Problems in Mathematical PhysicsThis PhD thesis deals with a number of different problems in mathematical physics with the common thread that they have probabilistic aspects. The problems all stem from mathematical studies of…Frederik Ravn Klausen·Dec 14, 2023SaveLearn
Spectral Moments of the real Ginibre ensembleThe moments of the real eigenvalues of real Ginibre matrices are investigated from the viewpoint of explicit formulas, differential and difference equations, and large N expansions. These topics…Sung-Soo Byun, Peter J. Forrester·Dec 14, 2023SaveLearn
Q-functions for lambda opersWe consider the Schr\"odinger operators which are constructed from the λ-opers corresponding to solutions of the sl2 Gaudin Bethe Ansatz equations. We define and study…Davide Masoero, Evgeny Mukhin, Andrea Raimondo·Dec 14, 2023SaveLearn
The massive modular Hamiltonian for a double coneThe Tomita-Takesaki modular operator for local algebras plays an important role in quantum field theory, and more recently in the study of relative entropy. However, the explicit expression of this…Daniela Cadamuro·Dec 13, 2023SaveLearn
A rigorous mathematical theory for topological phases and edge modes in spring-mass mechanical systemsIn this work, we examine the topological phases of the spring-mass lattices when the spatial inversion symmetry of the system is broken and prove the existence of edge modes when two lattices with…Ridvan Ozdemir, Junshan Lin·Dec 13, 2023SaveLearn
Discrete and embedded trapped modes in a plane quantum waveguide with a small obstacle: exact solutionsExact solutions describing trapped modes in a plane quantum waveguide with a small rigid obstacle are constructed in the form of convergent series in powers of the small parameter characterizing the…P. Zhevandrov, A. Merzon, M. I. Romero Rodríguez et al.·Dec 13, 2023SaveLearn
Orthonormal Strichartz estimates for Schr\"odinger operator and their applications to infinitely many particle systemsWe develop an abstract perturbation theory for the orthonormal Strichartz estimates, which were first studied by Frank-Lewin-Lieb-Seiringer. The method used in the proof is based on the duality…Akitoshi Hoshiya·Dec 13, 2023SaveLearn
Dixmier trace and the DOS of perturbed magnetic operatorsThe main goal of this work is to provide a description of the trace per unit volume in terms of the Dixmier trace (regularized by the resolvent of the harmonic oscillator) for a large class of…Fabian Belmonte, Giuseppe De Nittis·Dec 13, 2023SaveLearn
The Derivation of the Boltzmann Equation from Quantum Many-body DynamicsWe consider the quantum many-body dynamics at the weak-coupling scaling. We derive rigorously the quantum Boltzmann equation, which contains the classical hard sphere model and, effectively, the…Xuwen Chen, Justin Holmer·Dec 13, 2023SaveLearn
Counting mobiles by integrable systemsMobiles are a particular class of decorated plane trees which serve as codings for planar maps. Here we address the question of enumerating mobiles in their most general flavor, in correspondence…Michel Bergère, Bertrand Eynard, Emmanuel Guitter et al.·Dec 13, 2023SaveLearn
On periodic solutions and attractors for the Maxwell--Bloch equationsWe consider the Maxwell-Bloch system which is a finite-dimensional approximation of the coupled nonlinear Maxwell-Schr\"odinger equations. The approximation consists of one-mode Maxwell field coupled…Alexander Komech·Dec 13, 2023SaveLearn
Homogenization of 2D materials in the Thomas-Fermi-von Weizsacker theoryWe study the homogenization of the Thomas-Fermi-von Weizsacker (TFW) model for 2D materials. It consists in considering 2D-periodic nuclear densities with periods going to zero. We study the behavior…Saad Benjelloun, Salma Lahbabi, Abdelqoddous Moussa·Dec 13, 2023SaveLearn
Electrodynamics and Geometric Continuum MechanicsThis paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum…Reuven Segev·Dec 13, 2023SaveLearn
Wasserstein speed limits for Langevin systemsPhysical systems transition between states with finite speed that is limited by energetic costs. In this work, we derive bounds on transition times for general Langevin systems that admit a…Ralph Sabbagh, Olga Movilla Miangolarra, Tryphon T. Georgiou·Dec 12, 2023SaveLearn