Lab Home | Phone | Search
Center for Nonlinear Studies  Center for Nonlinear Studies
 Home 
 People 
 Current 
 Affiliates 
 Visitors 
 Students 
 Research 
 ICAM-LANL 
 Publications 
 Conferences 
 Workshops 
 Sponsorship 
 Talks 
 Colloquia 
 Colloquia Archive 
 Seminars 
 Postdoc Seminars Archive 
 Quantum Lunch 
 CMS Colloquia 
 Q-Mat Seminars 
 Q-Mat Seminars Archive 
 Archive 
 Kac Lectures 
 Dist. Quant. Lecture 
 Ulam Scholar 
 Colloquia 
 
 Jobs 
 Students 
 Summer Research 
 Visitors 
 Description 
 Past Visitors 
 Services 
 General 
 
 History of CNLS 
 
 Maps, Directions 
 CNLS Office 
 T-Division 
 LANL 
 
Wednesday, December 10, 2008
2:00 PM - 3:00 PM
CNLS Conference Room (TA-3, Bldg 1690)

Seminar

Weak ergodicity breaking

Eli Barkai
Bar-Ilan University

In nature the noisy signal representing a physical observable is in many cases unpredictable, though the long time average of the signal is identical to ensemble average (ergodicity). For this reason Boltzmann-Gibbs ergodic statistical mechanics is a powerful tool which gives predictions on time averages. Certain processes characterized by power law sojourn times, in such a way that the average waiting time in a state of the system is infinite are known to exhibit weak ergodicity breaking. For such scale free (in time) processes, time averages remain random even in the limit of long measurement time. The fundamental question is what statistical theory replaces standard ergodic statistical mechanics?

Recent examples of systems and models which exhibit weak ergodicity breaking include blinking quantum dots, anomalous diffusion of mRNA in the cell, the sub-diffusive continuous time random walk model, and the quenched trap model. In these diverse systems the distribution of waiting times in a micro-state of the system decays like a power law, with a diverging average sojourn time. For example blinking quantum dots have an on state in which many photons are emitted and an off state where the dot is in a dark state. The probability density function $\psi(t)$ of on and off times follows power law statistics with an average on and off time which is infinite $\psi(t)\sim t^{- (1 + \alpha)}$ and $0<\alpha<1$. Hence if we perform a time average it can never be made for long enough time to obtain ergodicity since the average on and off times diverge. A general theory of weak ergodicity is discussed and examples analyzed.

Host: Golan Bel, CCS-3/CNLS