Long-time asymptotics for open classical systems

Date

Nov 10, 2011

Time

2:50 PM - 3:50 PM

Speaker

Dr. Grigorios Pavliotis

Affiliation

Imperial College London

Series

TUD Mathematik AG Analysis & Stochastik

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Description

In this talk I will present some recent results on the long time asympotics of a small Hamiltonian system (the "distinguished particle") coupled to a heat bath which is modeled as an infinite dimensional Hamiltonian system with random initial conditions. After elimination of the heat bath variables, the dynamics of the distinguished particle can be described using a stochastic integrodifferential equation, the generalized Langevin equation (GLE). The GLE can then be approximated by a degenerate Markov process in an extended phase space. For this Markov process we prove exponentially fast convergence to equilibrium, a homogenization theorem (invariance principle), estimates on derivatives of the associated Markov semigroup and we also study several distinguished limits of physical interest. Applications of our results to MCMC (Markov Chain Monte Carlo) techniques are also discussed. Our proofs are based on a careful analysis of the spectrum of the generator of this Markov process, which is a hypoelliptic operator, and extensive use of the recently developed theory of hypocoercivity is made. This is joint work with Michela Ottobre and Karel Pravda-Starov.

Links

• Webseite der AG Analysis & Stochastik

Last modified: Nov 2, 2011, 11:58:45 AM