×

Nonergodic Brownian motion. (English) Zbl 1223.37008

The dynamics of non-Markovian generalized Langevin equations is studied. The authors obtain that the probability density function (PDF) of the system depends on the choice of the initial preparation. Non-ergodicity in non-Markovian Brownian dynamics of two classes is presented by means of the Boltzmann ergodic hypothesis condition. Moreover, the authors find that Lee’s condition for the integration over an autocorrelation function is not valid to non-Markovian Brownian dynamics.

MSC:

37A30 Ergodic theorems, spectral theory, Markov operators
37A50 Dynamical systems and their relations with probability theory and stochastic processes
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
PDFBibTeX XMLCite
Full Text: DOI