Related papers: Existence of equilibrium for Infinite System of In…
An algorithm is presented which computes a translationally invariant matrix product state approximation of the ground state of an infinite 1D system; it does this by embedding sites into an approximation of the infinite ``environment'' of…
A finite-volume scheme for a cross-diffusion model arising from the mean-field limit of an interacting particle system for multiple population species is studied. The existence of discrete solutions and a discrete entropy production…
In this paper we extend the local iterative Lie-Schwinger block-diagonalization method - introduced in [DFPR3] for quantum lattice systems with bounded interactions in arbitrary dimension- to systems with unbounded interactions, i.e.,…
The problem of the lattice diffusion of two particles coupled by a contact repulsive interaction is solved by finding analytical expressions of the two-body probability characteristic function. The interaction induces anomalous drift with a…
We consider limits of equilibrium distributions as temperature approaches zero, for systems of infinitely many particles, and characterize the support of the limiting distributions. Such results are known for particles with positions on a…
In many interacting particle systems, relaxation to equilibrium is thought to occur via the growth of 'droplets', and it is a question of fundamental importance to determine the critical length at which such droplets appear. In this paper…
Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions…
In this paper we propose a Monte Carlo method for generating finite-domain marginals of critical distributions of statistical models in infinite volume. The algorithm corrects the problem of the long-range effects of boundaries associated…
In this work, we investigate the dynamics of an inhomogeneous coupled nonlinear Schrodinger system with quadratic-type interactions. Such systems arise naturally in nonlinear dynamics and mathematical physics, particularly in nonlinear…
We provide a simple proof of the Lieb-Robinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which…
We introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface $I$. This system can be used to model the transport of positive and negative charges in a…
In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
We study a recently introduced formulation for fluid-structure interaction problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method. The time discretization of the problem leads to a mixed…
The purpose of this paper is to investigate the long time behaviour for a self-interacting diffusion and a self-interacting velocity jump process. While the diffusion case has already been studied for some particular potential function, the…
We discuss the form of the entropy for classical hamiltonian systems with long-range interaction using the Vlasov equation which describes the dynamics of a $N$-particle in the limit $N\to\infty$. The stationary states of the hamiltonian…
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…
In this article, we study the long-time behavior of a finite-volume discretization for a nonlinear kinetic reaction model involving two interacting species. Building upon the seminal work of [Favre, Pirner, Schmeiser, ARMA, 2023], we extend…
Continuum limits are a powerful tool in the study of many-body systems, yet their validity is often unclear when long-range interactions are present. In this work, we rigorously address this issue and put forth an exact representation of…