TY - JOUR
T1 - Weak ergodicity breaking in the continuous-time random walk
AU - Bel, G.
AU - Barkai, E.
PY - 2005/6/24
Y1 - 2005/6/24
N2 - The continuous-time random walk (CTRW) model exhibits a nonergodic phase when the average waiting time diverges. Using an analytical approach for the nonbiased and the uniformly biased CTRWs, and numerical simulations for the CTRW in a potential field, we obtain the nonergodic properties of the random walk which show strong deviations from Boltzmann-Gibbs theory. 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.
AB - The continuous-time random walk (CTRW) model exhibits a nonergodic phase when the average waiting time diverges. Using an analytical approach for the nonbiased and the uniformly biased CTRWs, and numerical simulations for the CTRW in a potential field, we obtain the nonergodic properties of the random walk which show strong deviations from Boltzmann-Gibbs theory. 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.
UR - http://www.scopus.com/inward/record.url?scp=27744586782&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.94.240602
DO - 10.1103/PhysRevLett.94.240602
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AN - SCOPUS:27744586782
SN - 0031-9007
VL - 94
JO - Physical Review Letters
JF - Physical Review Letters
IS - 24
M1 - 240602
ER -