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Weak ergodicity breaking in the continuous time random walk

Wednesday 28th June 2006 - 14:00 to 14:10
INI Seminar Room 1
The continuous-time random walk (CTRW) model exhibits a nonergodic phase when the average waiting time diverges. The first passage time probability density function for nonbiased and uniformly biased CTRWs is shown to yields the nonergodic properties of the random walk which show strong deviations from Boltzmann-Gibbs theory. Using numerical simulations we generalize the results for the CTRW in a potential field. We derive the distribution function of occupation times in a bounded region of space which in the ergodic phase recovers the Boltzmann-Gibbs theory, while in the nonergodic phase yields a generalized nonergodic statistical law.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons