Single-file dynamics with different diffusion constants.
We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have different diffusion constants. For the two-particle case an exact result for the conditional probability density function (PDF) is obtained for arbitrary initial particle positions and all times. The two-particle PDF is used to obtain the tagged particle PDF. For the general N-particle case (N large) we perform stochastic simulations using our new computationally efficient stochastic simulation technique based on the Gillespie algorithm. We find that the mean square displacement for a tagged particle scales as the square root of time (as for identical particles) for long times, with a prefactor which depends on the diffusion constants for the particles; these results are in excellent agreement with very recent analytic predictions in the mathematics literature.
Ambjörnsson
Tobias
T
Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. ambjorn@mit.edu
Lizana
Ludvig
L
Lomholt
Michael A
MA
Silbey
Robert J
RJ
D000465:Algorithms; D004058:Diffusion; D008956:Models, Chemical; D009038:Motion; D013269:Stochastic Processes; D013997:Time Factors