Prof. Eli Barkai 
Bar Ilan University

Date: Oct. 31, 2010

Title: Weak Ergodicity Breaking: From Blinking Quantum Dots to mRNA
Diffusion in the Cell

Abstract:

In nature the noisy signal representing a physical observable is in
many cases unpredictable, though the long time average of the signal
converges in statistical sense to the ensemble average (ergodicity).
Observations of dynamics of single particles, e.g. blinking quantum
dots, and mRNA sub-diffusing in a cell, revealed non-ergodic
processes.  Such processes are analyzed within the statistical
framework of weak ergodicity breaking. Foundations of the theory are
discussed based on random walk models, systems with L\'evy distributed
partition functions (e.g. the quenched trap model), and time
permitting dynamical systems with zero Lyapunov exponent.