On the Mixing of Diffusing Particles

Details On the Mixing of Diffusing Particles On the Mixing of Diffusing Particles

2010-10-13

arxiv.org/abs/1010.2563v1

Phys. Rev. E 82, 061103 (2010)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 6 figures, 2 tables

Scientific paper

10.1103/PhysRevE.82.061103

We study how the order of N independent random walks in one dimension evolves with time. Our focus is statistical properties of the inversion number m, defined as the number of pairs that are out of sort with respect to the initial configuration. In the steady-state, the distribution of the inversion number is Gaussian with the average ~N^2/4 and the standard deviation sigma N^{3/2}/6. The survival probability, S_m(t), which measures the likelihood that the inversion number remains below m until time t, decays algebraically in the long-time limit, S_m t^{-beta_m}. Interestingly, there is a spectrum of N(N-1)/2 distinct exponents beta_m(N). We also find that the kinetics of first-passage in a circular cone provides a good approximation for these exponents. When N is large, the first-passage exponents are a universal function of a single scaling variable, beta_m(N)--> beta(z) with z=(m-)/sigma. In the cone approximation, the scaling function is a root of a transcendental equation involving the parabolic cylinder equation, D_{2 beta}(-z)=0, and surprisingly, numerical simulations show this prediction to be exact.

Affiliated with

Also associated with

No associations

Rating

On the Mixing of Diffusing Particles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Mixing of Diffusing Particles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Mixing of Diffusing Particles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-226109