Asymptotic Analysis for Markovian models in non-equilibrium Statistical Mechanics

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Title: Asymptotic Analysis for Markovian models in non-equilibrium Statistical Mechanics
Author(s): Ottobre, Michela
Item Type: Thesis or dissertation
Abstract: 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.
Publication Date: 2011
Date Awarded: Jul-2012
URI: http://hdl.handle.net/10044/1/9797
Advisor: Pavliotis, Greg
Department: Mathematics
Publisher: Imperial College London
Qualification Level: Doctoral
Qualification Name: Doctor of Philosophy (PhD)
Appears in Collections:Mathematics PhD theses



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