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.
Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:560616 |
Date | January 2012 |
Creators | Ottobre, Michela |
Contributors | Pavliotis, Greg |
Publisher | Imperial College London |
Source Sets | Ethos UK |
Detected Language | English |
Type | Electronic Thesis or Dissertation |
Source | http://hdl.handle.net/10044/1/9797 |
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