Related papers: Lenard-Balescu thermalization: rigorous derivation…
This article is devoted to the long-time dynamics of point-vortex type systems near thermal equilibrium and to the possible emergence of collisional relaxation. More precisely, we consider a tagged particle coupled to a large number of…
We review and complete the existing literature on the kinetic theory of spatially homogeneous systems with long-range interactions taking collective effects into account. The evolution of the system as a whole is described by the…
We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal…
In the mean-field regime, the evolution of a gas of $N$ interacting particles is governed in first approximation by a Vlasov type equation with a self-induced force field. This equation is conservative and describes return to equilibrium…
We develop a kinetic theory of systems with long-range interactions taking collective effects and spatial inhomogeneity into account. Starting from the Klimontovich equation and using a quasilinear approximation, we derive a…
This paper gives the first full proof of the justification of the linear Boltzmann equation from an underlying long range particle evolution. We suppose that a tagged particle is interacting with a background via a two body potential that…
A stochastic treatment yielding to the derivation of a general Fokker-Planck equation is presented to model the slow convergence towards equilibrium of mean-field systems due to finite-N effects. The thermalization process involves notably…
We discuss the dynamics and thermodynamics of systems with long-range interactions. We contrast the microcanonical description of an isolated Hamiltonian system to the canonical description of a stochastically forced Brownian system. We…
Finite-temperature one-loop renormalization of the Standard Model, coupled with dynamic metric, is conducted in this study. The entire analysis is coherently carried out by using the refined background field method, applied in the spirit of…
We complete the kinetic theory of inhomogeneous systems with long-range interactions initiated in previous works. We use a simpler and more physical formalism. We consider a system of particles submitted to a small external stochastic…
The Balescu-Lenard equation from plasma physics is widely considered to include a highly accurate correction to Landau's fundamental collision operator. Yet so far it has seen very little mathematical study. We perform an extensive…
We consider a particle in the harmonic approximation coupled linearly to an environment. modeled by an infinite set of harmonic oscillators. The system (particle--environment) is considered in a cavity at thermal equilibrium. We employ the…
We study a diffuse-interface model for thermally driven phase separation in viscous incompressible mixtures. The system couples a convective Cahn-Hilliard equation for the order parameter with a Stokes subsystem for the velocity-pressure…
Long-range interacting systems unavoidably relax through Poisson shot noise fluctuations generated by their finite number of particles, $N$. When driven by two-body correlations, i.e. ${1/N}$ effects, this long-term evolution is described…
Finite-$N$ effects unavoidably drive the long-term evolution of long-range interacting $N$-body systems. The Balescu-Lenard kinetic equation generically describes this process sourced by ${1/N}$ effects but this kinetic operator exactly…
The importance of implementing a proper regularization procedure in order to treat thermo and magnetic contributions within nonrenormalizable theories is investigated. Our study suggests that potential divergences should be isolated into…
We study an interacting system of $N$ classical particles on a line at thermal equilibrium. The particles are confined by a harmonic trap and repelling each other via pairwise interaction potential that behaves as a power law $\propto…
It is shown that a paradigm of classical statistical mechanics --- the thermalization of a Brownian particle --- has a low-dimensional, deterministic analogue: when a heavy, slow system is coupled to fast deterministic chaos, the resultant…
We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice, in the presence of thermal noise. The internal degree of freedom of each particle is a periodic…
We propose a new mathematical tool for the study of transport properties of models for lattice vibrations in crystalline solids. By replication of dynamical degrees of freedom, we aim at a new dynamical system where the "local" dynamics can…