The standard description of Fermi acceleration, developing in a class of time-dependent billiards, is given in terms of a diffusion process taking place in momentum space. Within this framework, the evolution of the probability density function (PDF) of the magnitude of particle velocities as a function of the number of collisions n is determined by the Fokker-Planck equation (FPE). In the lite...

Abstract. The paper deals with the diffusion approximation of the Boltzmann equation for semiconductors in the presence of spatially oscillating electrostatic potential. When the oscillation period is of the same order of magnitude as the mean free path, the asymptotics leads to the Drift-Diffusion equation with a homogenized electrostatic potential and a diffusion matrix involving the small sc...

The probability that a particle, crossing the shock along a given direction, be reflected backwards along another direction, was shown to be the key element in determining the spectrum of non–thermal particles accelerated via Fermi mechanism around a shock. Here an explicit equation for this probability distribution is given, for both the upstream and downstream sections. Though analytically in...

The probability that a particle, crossing the shock along a given direction, be reflected backwards along another direction, was shown to be the key element in determining the spectrum of non–thermal particles accelerated via Fermi mechanism around a shock. Here an explicit equation for this probability distribution is given, for both the upstream and downstream sections. Though analytically in...

We present a numerical study of mixed boson-fermion systems at zero temperature in isotropic and anisotropic harmonic traps. We investigate the phenomenon of component separation as function of the strength of the interparticle interaction. While solving a Gross-Pitaevskii mean field equation for the boson distribution in the trap, we utilize two different methods to extract the density profile...

We consider the evolution of small amplitude, long wavelength initial data by a polyatomic Fermi–Pasta–Ulam lattice differential equation whose material properties vary periodically. Using the methods of homogenization theory, we prove rigorous estimates that show that the solution breaks up into the linear superposition of two appropriately scaled and modulated counterpropagating waves, each o...

This paper presents the Thomas-Fermi approach generalized to consider the particle correlations in many-body systems with non-Coulomb interaction potentials. The key points of the generalization consist in using integral formulation and extracting the pair distribution function. The latter has been found to obey the integral equation which, in the classical limit, is reduced to the well-known e...

A method for the description of spin-isospin phase transitions in nuclear matter is developed. It aliows a complete description of the pion condensation phase transition in the framework of the Landau-Migdal Fermi liquid theory. The equation of the order Parameter is derived and the condensation energy is calculated. We study the influence of pion condensation on the nuclear equation of state a...

Assuming that the maximal allowed number of identical particles in a state is an integer parameter, q, we derive the statistical weight and analyze the associated equation that defines the statistical distribution. The derived distribution covers Fermi-Dirac and Bose-Einstein ones in the particular cases q=1 and q--> infinity (n(i)/q-->1), respectively. We show that the derived statistical weig...