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Title: Asymptotic analysis for Markovian models in non-equilibrium statistical mechanics
Author: Ottobre, Michela
ISNI:       0000 0004 2727 9670
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2012
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This thesis is mainly concerned with the problem of exponential convergence to equilibrium for open classical systems. We consider a model of a small Hamiltonian system coupled to a heat reservoir, which is described by the Generalized Langevin Equation (GLE) and we focus on a class of Markovian approximations to the GLE. The generator of these Markovian dynamics is an hypoelliptic non-selfadjoint operator. We look at the problem of exponential convergence to equilibrium by using and comparing three different approaches: classic ergodic theory, hypocoercivity theory and semiclassical analysis (singular space theory). In particular, we describe a technique to easily determine the spectrum of quadratic hypoelliptic operators (which are in general non-selfadjoint) and hence obtain the exact rate of convergence to equilibrium.
Supervisor: Pavliotis, Greg Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral