Diffusion of Finite-Sized Hard-Core Interacting Particles In a One-Dimensional Box - Tagged Particle Dynamics - Condensed Matter > Statistical Mechanics

Diffusion of Finite-Sized Hard-Core Interacting Particles In a One-Dimensional Box - Tagged Particle Dynamics - Condensed Matter > Statistical Mechanics - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We solve a non-equilibrium statistical mechanics problem exactly, namely, thesingle-file dynamics of N hard-core interacting particles the particles cannotpass each other of size \Delta diffusing in a one dimensional system of finitelength L with reflecting boundaries at the ends. We obtain an exact expressionfor the conditional probability density function P Ty T,t|y {T,0} that atagged particle T T=1,

.,N is at position y T at time t given that it attime t=0 was at position y {T,0}. Going beyond previous studies, we considerthe asymptotic limit of large N, maintaining L finite, using a non-standardasymptotic technique. We derive an exact expression for P Ty T,t|y {T,0} fora a tagged particle located roughly in the middle of the system, from which wefind that there are three time regimes of interest for finite-sized systems:A For times much smaller than the collision time t<< t coll=1- ho^2D,where ho=N-L is the particle concentration and D the diffusion constant foreach particle, the tagged particle undergoes normal diffusion; B for timesmuch larger than the collision time t>> t coll but times smaller than theequilibrium time t<< t eq=L^2-D we find a single-file regime whereP Ty T,t|y {T,0} is a Gaussian with a mean square displacement scaling ast^{1-2}; C For times longer than the equilibrium time \$t>> t eq,P Ty T,t|y {T,0} approaches a polynomial-type equilibrium probability densityfunction.

Autor: Ludvig Lizana, Tobias Ambjornsson

Fuente: https://arxiv.org/