caa a22 4500 467892091 CHVBK 20180406152752.0 cr unu---uuuuu 170328e20060501xx s 000 0 eng 10.1007/s10955-006-9109-8 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9109-8 Barkai E. Department of Physics, Bar Ilan University, 52900, Ramat-Gan, Israel aut Residence Time Statistics for Normal and Fractional Diffusion in a Force Field [Elektronische Daten] [E. Barkai] We investigate statistics of occupation times for an over-damped Brownian particle in an external force field, using a backward Fokker-Planck equation introduced by Majumdar and Comtet. For an arbitrary potential field the distribution of occupation times is expressed in terms of solutions of the corresponding first passage time problem. This general relationship between occupation times and first passage times, is valid for normal Markovian diffusion and for non-Markovian sub-diffusion, the latter modeled using the fractional Fokker-Planck equation. For binding potential fields we find in the long time limit ergodic behavior for normal diffusion, while for the fractional framework weak ergodicity breaking is found, in agreement with previous results of Bel and Barkai on the continuous time random walk on a lattice. For non-binding cases, rich physical behaviors are obtained, and classification of occupation time statistics is made possible according to whether or not the underlying random walk is recurrent and the averaged first return time to the origin is finite. Our work establishes a link between fractional calculus and ergodicity breaking. Springer Science+Business Media, Inc., 2006 Weak ergodicity breaking nationallicence Fractional calculus nationallicence Backward Fokker-Planck equation nationallicence Occupation times nationallicence Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/4(2006-05-01), 883-907 0022-4715 123:4<883 2006 123 10955 https://doi.org/10.1007/s10955-006-9109-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9109-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Barkai E. Department of Physics, Bar Ilan University, 52900, Ramat-Gan, Israel aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/4(2006-05-01), 883-907 0022-4715 123:4<883 2006 123 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer