Related papers: Theorem on the Distribution of Short-Time Particle…
The distribution of the initial very short-time displacements of a single particle is considered for a class of classical systems with Gaussian initial velocity distributions and arbitrary initial particle positions. A very brief sketch is…
A recent theorem giving the initial behavior of very short-time fluctuations of particle displacements in classical many-body systems is discussed. It has applications to equilibrium and non-equilibrium systems, one of which is a series…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
We examine the structure of the distribution of single particle displacements (van-Hove function) in a broad class of materials close to glass and jamming transitions. In a wide time window comprising structural relaxation, van-Hove…
In this work we present a general derivation of the non-Fickian behavior for the self-diffusion of identically interacting particle systems with excluded mutual passage. We show that the conditional probability distribution of finding a…
Active particles self-propel themselves with a stochastically evolving velocity, generating a persistent motion leading to a non-diffusive behavior of the position distribution. Nevertheless, an effective diffusive behavior emerges at times…
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…
Non-Gaussian nature of the probability distribution of particles' displacements in the supercooled temperature regime in glass-forming liquids are believed to be one of the major hallmarks of glass transition. It is already been established…
We consider a Hamiltonian system of particles, interacting through of a smooth pair potential. We look at the system on a space scale of order {\epsilon}^1, times of order {\epsilon}^2, and mean velocities of order {\epsilon}, with…
It is demonstrated that the canonical distribution for a subsystem of a closed system follows directly from the solution of the time-reversible Newtonian equation of motion in which the total energy is strictly conserved. It is shown that…
In this paper we present a new model for modeling the diffusion and relative dispersion of particles in homogeneous isotropic turbulence. We use an Heisenberg-like Hamiltonian to incorporate spatial correlations between fluid particles,…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
We investigate the two-dimensional classical dynamics of the scattering of point particles by two periodically oscillating disks. The dynamics exhibits regular and chaotic scattering properties, as a function of the initial conditions and…
We consider the wide class of few-particle systems that have some analog of the thermodynamic laws. These systems are characterized by the distributions that are determined by the Hamiltonian and satisfy the Liouville equation. Few-particle…
The principles of behavior of the system with discrete interactions are applied to description of motion of the relativistic particle. Applying the concept of non-local behavior both to position in space and to time, the apparently…
While 2D Gibbsian particle systems might exhibit orientational order resulting in a lattice-like structure, these particle systems do not exhibit positional order if the interaction between particles satisfies some weak assumptions. Here we…
Nonequilibrium behaviors of positional order are discussed based on diffusion processes in particle systems. With the cumulant expansion method up to the second order, we obtain a relation between the positional order parameter $\Psi$ and…
Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the "active" particle is driven along…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
We consider a system of $N$ interacting particles, described by SDEs driven by Poisson random measures, where the coefficients depend on the empirical measure of the system. Every particle jumps with a jump rate depending on its position.…