Related papers: Convergence to equilibrium due to collisions with …
A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. The statistical mechanics of such a system is derived…
We consider general hamiltonian systems with quadratic interaction potential and $N<\infty$ degrees of freedom, only $m$ of which have contact with external world, that is subjected to damping and random stationary external forces. We show…
We investigate the behaviour of a system of particles with the different character of interaction. The approach makes it possible to describe systems of interacting particles by statistical methods taking into account a spatial…
We define a notion of coupling time with ambiguities for interacting particle systems, and show how this can be used to prove ergodicity and to bound the convergence time to equilibrium and the decay of correlations at equilibrium. A…
We consider the dynamics of finite systems of point masses which move along the real line. We suppose the particles interact pairwise and undergo perfectly inelastic collisions when they collide. In particular, once particles collide, they…
We consider a class of $d$-dimensional stochastic differential equations that model a non-colliding random particle system. We provide a sufficient condition, which does not depend on the dimension $d$, for the existence of negative moments…
At time zero, there are $N$ identical point particles in the line (1D) which are characterized by their positions and velocities. Both values are given randomly and independently from each other, with arbitrary probability densities. Each…
A systematic structure of particle interactions is predicted within and beyond the standard model. The proof is performed either on the basis of (A) a generalisable form of general relativity or, equivalently, (B) minimum information…
The theoretical cornerstone of statistical mechanics is the ergodic assumption that all accessible configurations of a physical system are equally likely. Here we show how such property arises when an open quantum system is continuously…
Consider a system of $N$ particles interacting through Newton's second law with Coulomb interaction potential in one spatial dimension or a $\mathcal{C}^2$ smooth potential in any dimension. We prove that in the mean field limit $N \to +…
Normally, in mathematics and physics, only point particle systems, which are either finite or countable, are studied. We introduce new formal mathematical object called regular continuum system of point particles (with continuum number of…
The trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck equation in the presence of a convex external potential, without smallness restriction on the interaction. From this are…
The thermodynamic equilibrium conditions for compact structures composed by mass varying particles are discussed assuming that the so-called dynamical mass behaves like an additional extensive thermodynamic degree of freedom. It then…
Heavy ion collisions at ultrarelativistic energies offer the opportunity to study the irreversibility of multiparticle processes. Together with the many-body decays of resonances, the multiparticle processes cause the system to evolve…
In a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to any point of the available phase space after a long time, filling it uniformly. Using Born's rules to connect quantum states with probabilities,…
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…
In relativistic quantum mechanics, elementary particles are described by irreducible unitary representations of the Poincare group. The same applies to the center-of-mass kinematics of a multi-particle system that is not subject to external…
We consider a system of charged particles moving on the real line driven by electrostatic interactions. Since we consider charges of both signs, collisions might occur in finite time. Upon collision, some of the colliding particles are…
We prove H\"{o}lder regularity for the trajectories of an interacting particle system. The particle velocities are given by the nonlocal and singular interactions with the other particles. Particle collisions occur in finite time. Prior to…
Consider a finite system of competing Brownian particles on the real line. Each particle moves as a Brownian motion, with drift and diffusion coefficients depending only on its current rank relative to the other particles. We find a…