Related papers: N particles approximation of the Vlasov equations …
A continuous infinite system of point particles with strong superstable interaction is considered in the framework of classical statistical mechanics. The family of approximated correlation functions is determined in such a way, that they…
This paper outlines a variety of possible applications of the Vlasov equation and its generalization, i.e., the Klimontovich equation, in various areas of many-body physics. In particular, these equations are shown to be used in…
For the generalized statistical mechanics based on the Tsallis entropy, a variational perturbation approximation method with the principle of minimal sensitivity is developed by calculating the generalized free energy up to the third order…
The universal mechanism of trapping and localization of sufficiently slow-speed particles by a potential well deepening with time is established on the basis of fundamental relations of classical mechanics. Such wells may be created for a…
This paper reviews Vlasov-based numerical methods used to model plasma in space physics and astrophysics. Plasma consists of collectively behaving charged particles that form the major part of baryonic matter in the Universe. Many concepts…
We provide sufficient conditions for the existence of periodic solutions of the of the Lorentz force equation, which models the motion of a charged particle under the action of an electromagnetic fields. The basic assumptions cover relevant…
The velocity of a passive particle in a one-dimensional wave field is shown to converge in law to a Wiener process, in the limit of a dense wave spectrum with independent complex amplitudes, where the random phases distribution is invariant…
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…
The uniformly valid approximation to solutions of the radial Schr\"odinger equation with power-law potentials are obtained by means of the explicit summation of the leading constituent WKB series.
We consider optimization problems for interacting particle systems. We show that critical points solve a Vlasov equation, and that in general no minimizers exist despite continuity of the action functional. We prove an explicit…
We calculate the energy of the state closest to threshold for two and three identical, spinless particles confined to a cubic spatial volume with periodic boundary conditions and with zero total momentum in the finite-volume frame. The…
An analytical solution of the selfconsistent Vlasov equation is presented. The time evolution is entirely determined by the initial distribution function. The largest Lyapunov exponent is calculated analytically. For special parameters of…
The one-dimensional motion of any number $\cN$ of particles in the field of many independent waves (with strong spatial correlation) is formulated as a second-order system of stochastic differential equations, driven by two Wiener…
We show that for nanoparticles with giant polarizability $\alpha$ (a prominent example being the recently studied Na$_{14}$F$_{13}$ molecular clusters) van der Waals forces are significantly enhanced at interparticle distances shorter than…
This paper deals with the existence and uniqueness of solutions to kinetic equations describing alignment of self-propelled particles. The particularity of these models is that the velocity variable is not on the euclidean space but…
Using the approach to quantum entanglement based on the quantum fluctuations of observables, we show the existence of perfect entangled states of a single "spin-1" particle. We give physical examples related to the photons, condensed matter…
In this paper we prove approximation properties of the solutions of the defoucsing NLS equation on the circle by nearly linear flows. In addition we show that spatially periodic solutions of the defocusing NLS equation evolving in…
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…
This article is concerned with the kinetic modeling, by means of the Vlasov equation, of charged particles under the influence of a strong external electromagnetic field, i.e. when epsilon^2, the dimensionless cyclotron period, tends to…
We present a purely probabilistic proof of propagation of molecular chaos for $N$-particle systems in dimension $3$ with interaction forces scaling like $1/\vert q\vert^{\lambda}$ with $\lambda<2$ and cut-off at $q = N^{-1/3}$. The proof…