Seminars of the Focus Area Complex Systems

Prof. Dr. C. Beta, Prof. Dr. K. Dethloff, Prof. Dr. R. Engbert, Prof. Dr. M. Holschneider, Prof. Dr. W. Huisinga, Prof. Dr. Ralf Metzler, Prof. Dr. A. Pikovsky, Prof. Dr. S. Reich, Prof. Dr. M. Rosenblum, Prof. Dr. G. Rüdiger, Prof. Dr. T. Scheffer, Prof. Dr. F. Scherbaum, Prof. Dr. J. Selbig, Prof. Dr. F. Spahn


Speaker: Ralf Toenjes, Statistical Physics and Theory of Chaos, Inst. f. Physik und Astronomie, Uni Potsdam

Title: Non-Spectral Relaxation in the Levy-Ornstein-Uhlenbeck Process * Oberseminar Nichtlineare Dynamik

Time: Mon, Jan 21, 2013, 4pm

Place: bldg 28, room 0.104

It is well known, that the Fokker-Planck equation (FPE) describing the evolution of the probability density for a one dimensional Gaussian diffusion process in a potential can be mapped to a Schroedinger-like equation. Relaxation of expected values and autocorrelation functions are supposed to occur at rates given by the eigenvalues of the Hamiltonian. We show, that the fractional Fokker-Planck equation corresponding to a Levy-flight in a harmonic potential (Levy OU-process) can be mapped to the non-fractional FPE of a Gaussian OU-process and hence also to the Schroedinger equation of a quantum harmonic oscillator. However, the relaxation of bounded observables and their autocorrelation functions occurs in general not at rates given by its harmonic spectrum. This is even the case in the Gaussian-OU process, where broad initial distributions may relax much slower to the stationary distribution than predicted by the smallest harmonic relaxation rate. The linear Levy-Ornstein-Uhlenbeck process serves as a completely solvable example for this effect of non-spectral relaxation.

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Udo Schwarz, Zentrum für Dynamik komplexer Systeme,
Universität Potsdam, Campus Golm Karl-Liebknecht-Str. 24, 14476 Potsdam, building 28, room 2.107
Phone: (+49-331) 977-1658, Fax : (+49-331) 977-1045

Email: Udo.Schwarz AT

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