Hamiltonian models for the Madelung fluid and generalized Langevin equations

SIGLEAvailable from Bielefeld Univ. (DE). Forschungszentrum Bielefeld-Bochum-Stochastik (BiBoS) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Hyperbolic diffusion in chaotic systems

We consider a deterministic process described by a discrete one-dimensional chaotic map and study its diffusive-like properties. Starting with the corresponding Frobenius-Perron equation we derive an approximate evolution equation for the probability distribution which is a partial differential equation of a hyperbolic type. Consequently, the process is correlated, non-Markovian, non-Gaussian and the information propagates with a finite velocity. This is in clear contrast to conventional diffusion processes described by a standard parabolic diffusion equation with an infinite velocity of information propagation. Our approach allows for a more complete characterisation of diffusion dynamics of deterministic systems