Seminar - From Fickian diffusion to fractional Klein-Kramers equation: what to worry about and why

Seminar by

Alexander V. Milovanov

ENEA CR Frascati, Italy and IKI RAS Moscow, Russia


In this talk I briefly review the theoretical foundations of the diffusion (Fickian style) problem, then pass to more general statistical models allowing for sub- and super-diffusion, among these models are continuous time random walks and kinetic equations driven by stochastic noises (Gaussian, Lévy). In this fashion I shall introduce the Klein-Kramers equation (both standard and fractional) for relaxation dynamics in phase space, then consider a reduction of this equation to the Einstein-Smoluchowski equation (in the high-friction, long-time limit). In the second part of my talk I turn to fusion physics and very specifically to transport problems pertaining to the plasma staircase. This offers a platform to discuss the localization problem for Lévy flights and to introduce the theoretical concept of weak localization. Some results from recent comprehensive gyro-kinetic simulations of avalanche transport across the staircase transport barriers will be also shown (and briefly discussed).



tir 30 nov 21


DTU Fysik


DTU Lyngby Campus
Bygning 306
Auditorium 32