Berlin 2005 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 43: Einstein Symposium Brownian Motion, Diffusion and Beyond (SYBM) – Contributed Talks I

DY 43.2: Vortrag

Dienstag, 8. März 2005, 14:45–15:00, TU H2032

Brownian motion: Some puzzles 100 Years after Einstein and Smoluchowski — •Peter Hänggi — Institut für Physik, Universität Augsburg, Universitästrasse 1

The description of Brownian motion is well understood 100 years after Einstein and Smoluchowski. The stochastic process that describes Brownian motion in thermal equilibrium is a Gaussian. In classical statistical mechanics it is known as the Wiener process that can be derived from microscopic description in terms of a harmonic bath with a continuous spectrum for the bath-oscillator frequencies. The issue is more complex on a quantum level where the Brownian noise becomes operator-valued. Some open problems on the issue of Brownian motion remain nevertheless. These are: (1) the relaxation of an open quantum system in contact with a thermal heat bath that is prepared at initial time with some arbitrary correlation is still poorly understood (role of entanglement between bath and system under time evolution). Almost all literature treats the case of a Feynman-Vernon preparation where the system and the bath are not correlated at initial time. (2) The role of Brownian motion in systems exhibiting aging is not clear. (3) Another open problem is the problem of relativistic Brownian motion. For the latter area there exist practically no publications. In my talk I will review the state of the art and point out an Ansatz for solving the issues raised with points (1) and (2). For point (3), I will present a partial solution [1]. Moreover, I point out why the relativistic issue in its full generality will remain unsolved. [1]J. Dunkel and P. Hänggi, Theory of relativistic Brownian motion: The (1+1)-dimensional case, Phys. Rev. E 70, XXXXXX (2004), in press.