Variable separation without preselection and non-spectral relaxation in Fokker-Planck and generalized Fokker-Planck equations

The relaxation of a dissipative system to its equilibrium state often shows a multiexponential pattern with relaxation rates, which are typically considered to be independent of the initial condition. The rates follow from the spectrum of a Hermitian operator obtained by a similarity transformation of the initial Fokker-Planck operator. However, some initial conditions are mapped by this similarity transformation to functions which grow at infinity. These cannot be expanded in terms of the eigenfunctions of a Hermitian operator, and show different relaxation patterns. Such situations are exotic for Gaussian noises but are the rule in the Levy case. Being left without such a powerful tool of theoretical analysis of such systems as spectral decomposition, we have to look for alternatives.

DFG Programme Research Grants

International Connection Russia

Partner Organisation Russian Foundation for Basic Research

Participating Person Professor Eugene B. Postnikov, Ph.D.