Section: New Results

Stochastic acceleration and approach to equilibrium

S. De Bièvre and E. Soret rigorously proved the growth rate of the energy in a Markovian model for stochastic acceleration of a particle in a random medium, cf. [67] and [7] .

S. De Bièvre, Carlos Mejia-Monasterio (Madrid) and Paul E. Parris (Missouri)  [49] studied thermal equilibration in a two-component Lorentz gas, in which the obstacles are modeled by rotating disks. They show that a mechanism of dynamical friction leads to a fluctuation-dissipation relation that is responsible for driving the system to equilibrium.

Stephan De Bièvre, JeremyFaupin (Metz) and Schuble (Metz) [32] studied a related model quantum mechanically. Here a quantum particle moves through a field of quantized bose fields, modeling membranes that exchange energy and momentum with the particle. They establish a number of spectral properties of this model, that will be essential to study the time-asymptotic behavior of the system.