Related papers: Singular mean-field limits for fluctuations around…
A first-principles treatment of the vibrational dynamics of molecular chemisorbates on metal surfaces is presented. It is shown that the mean field quantum evolution of the vibrational position operator is determined by a quantum Langevin…
We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games…
Many natural phenomena are effectively described by interacting particle systems, which can be modeled using either deterministic or stochastic differential equations (SDEs). In this study, we specifically investigate particle systems…
The linear response of non-equilibrium systems with Markovian dynamics satisfies a generalized fluctuation-dissipation relation derived from time symmetry and antisymmetry properties of the fluctuations. The relation involves the sum of two…
We examine the fluctuations of the empirical density measure for the colour version of the symmetric nearest neighbour zero range particle systems in dimension one. We show that the weak limit of these fluctuations is the solution of a…
Predicting how systems respond to external perturbations far from equilibrium remains a fundamental challenge across physics, chemistry, and biology. We present a unified response framework for stochastic Markov dynamics that integrates…
Gravitational and electrostatic interactions are fundamental examples of systems with long-range interactions. Equilibrium properties of simple models with long-range interactions are well understood and exhibit exotic behaviors : negative…
We study a general asymptotic behavior of critical points of a diffused interface energy with a fixed contact angle condition defined on a domain $\Omega \subset \mathbb{R}^n$. We show that the limit varifold derived from the diffused…
We study the massless field on $D_n = D \cap \tfrac{1}{n} \Z^2$, where $D \subseteq \R^2$ is a bounded domain with smooth boundary, with Hamiltonian $\CH(h) = \sum_{x \sim y} \CV(h(x) - h(y))$. The interaction $\CV$ is assumed to be…
We consider a class of weakly interacting particle systems of mean-field type. The interactions between the particles are encoded in a graph sequence, i.e., two particles are interacting if and only if they are connected in the underlying…
The dynamics of fluctuations is considered for electrons near a positive ion or for charges in a confining trap. The stationary nonuniform equilibrium densities are discussed and contrasted. The linear response function for small…
In this work, we prove the well--posedness of a singularly interacting stochastic particle system and we establish propagation of chaos result towards the one-dimensional parabolic-parabolic Keller-Segel model.
The weak coupling limit for a quantum system, with discrete energy spectrum, coupled to a Bose reservoir with the most general linear interaction is considered: under this limit we have a quantum noise processes substituting for the field.…
The physical meaning, the properties and the consequences of a discrete scalar field are discussed; limits for the validity of a mathematical description of fundamental physics in terms of continuous fields are a natural outcome of discrete…
We establish a connection between tagged particles and size-biased empirical processes in interacting particle systems, in analogy to classical results on the propagation of chaos. In a mean-field scaling limit, the evolution of the…
A solution to the long-standing problem of identifying the conformal field theory governing the transition between quantized Hall plateaus of a disordered noninteracting 2d electron gas, is proposed. The theory is a nonlinear sigma model…
In this paper we derive a two dimensional spray model with gyroscopic effects as the mean-field limit of a system modeling the interaction between an incompressible fluid and a finite number of solid particles. This spray model has been…
We consider a class of linear-quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex…
The quantum dynamics of a subset of interacting bosons in a subspace of fixed particle number is described in terms of symmetrized many-particle states. A suitable partial trace operation over the von Neumann equation of an $N$-particle…
Central spin systems, in which a {\it central} spin is singled out and interacts nonlocally with several {\it bath} spins, are paradigmatic models for nitrogen-vacancy centers and quantum dots. They show complex emergent dynamics and…