21 research outputs found
Stochastic dynamics beyond the weak coupling limit: thermalization
We discuss the structure and asymptotic long-time properties of coupled
equations for the moments of a Brownian particle's momentum derived
microscopically beyond the lowest approximation in the weak coupling parameter.
Generalized fluctuation-dissipation relations are derived and shown to ensure
convergence to thermal equilibrium at any order of perturbation theory.Comment: 6+ page
Hitchhiking transport in quasi-one-dimensional systems
In the conventional theory of hopping transport the positions of localized
electronic states are assumed to be fixed, and thermal fluctuations of atoms
enter the theory only through the notion of phonons. On the other hand, in 1D
and 2D lattices, where fluctuations prevent formation of long-range order, the
motion of atoms has the character of the large scale diffusion. In this case
the picture of static localized sites may be inadequate. We argue that for a
certain range of parameters, hopping of charge carriers among localization
sites in a network of 1D chains is a much slower process than diffusion of the
sites themselves. Then the carriers move through the network transported along
the chains by mobile localization sites jumping occasionally between the
chains. This mechanism may result in temperature independent mobility and
frequency dependence similar to that for conventional hopping.Comment: a few typos correcte
Transient rectification of Brownian diffusion with asymmetric initial distribution
In an ensemble of non-interacting Brownian particles, a finite systematic
average velocity may temporarily develop, even if it is zero initially. The
effect originates from a small nonlinear correction to the dissipative force,
causing the equation for the first moment of velocity to couple to moments of
higher order. The effect may be relevant when a complex system dissociates in a
viscous medium with conservation of momentum
Generalized Fokker-Planck equation, Brownian motion, and ergodicity
Microscopic theory of Brownian motion of a particle of mass in a bath of
molecules of mass is considered beyond lowest order in the mass ratio
. The corresponding Langevin equation contains nonlinear corrections to
the dissipative force, and the generalized Fokker-Planck equation involves
derivatives of order higher than two. These equations are derived from first
principles with coefficients expressed in terms of correlation functions of
microscopic force on the particle. The coefficients are evaluated explicitly
for a generalized Rayleigh model with a finite time of molecule-particle
collisions. In the limit of a low-density bath, we recover the results obtained
previously for a model with instantaneous binary collisions. In general case,
the equations contain additional corrections, quadratic in bath density,
originating from a finite collision time. These corrections survive to order
and are found to make the stationary distribution non-Maxwellian.
Some relevant numerical simulations are also presented
Crossover from percolation to diffusion
A problem of the crossover from percolation to diffusion transport is
considered. A general scaling theory is proposed. It introduces
phenomenologically four critical exponents which are connected by two
equations. One exponent is completely new. It describes the increase of the
diffusion below percolation threshold. As an example, an exact solution of one
dimensional lattice problem is given. In this case the new exponent .Comment: 10 pages, 1 figur
Does a Brownian particle equilibrate?
PACS. 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion. PACS. 05.20.-y – Classical statistical mechanics. Abstract. – The conventional equations of Brownian motion can be derived from the first principles to order λ 2 = m/M, where m and M are the masses of a bath molecule and a Brownian particle respectively. We discuss the extension to order λ 4 using a perturbation analysis of the Kramers-Moyal expansion. For the momentum distribution such method yields an equation whose stationary solution is inconsistent with Boltzmann-Gibbs statistics. This property originates entirely from non-Markovian corrections which are negligible in lowest order but contribute to order λ 4. Dynamical justification of equilibrium statistical mechanics is a long-standing problem which can be traced to Einstein’s criticism of the statistical definition of probability of macrostates [1]. The renewed interest stems primarily from recent development in the theory of nonextensive systems for which the validity of classical Boltzmann-Gibbs (BG) statistics is not obvious. A number of dynamical models generating non-canonical distributions have been suggested lately [2], but for a truly conservative Hamiltonian system deviations from th