Weak ergodicity breaking in the continuous time random walk
Seminar Room 1, Newton Institute
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.