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Large deviations of observables in classical and quantum lattice spin systems
Abstract
In this thesis we explore large deviations for observables in classical and quantum lattice spin systems. In particular, we establish our results in the case where the Gibbs state of a fixed interaction is the probability measure. Thus, the results speak to describing the probability of finding the lattice in rare states, contrary to the equilibrium. We also present some examples to standard classical and quantum models. In the classical case, we establish our results by a direct construction, which avoids the smoothness issues associated to the Gärtner-Ellis Theorem. It also provides a direct look at how to establish this result without having to appeal to a level three, empirical large deviations result. In the quantum case, we extend the ideas of the classical construction and show both what you can and cannot establish in this case. We describe the addition assumptions needed to get around the noncommutativity issues that arise. The quantum results represent a significant contribution in trying to better understand this difficult case.
Subject Area
Mathematics
Recommended Citation
Diehl, Michael Anthony, "Large deviations of observables in classical and quantum lattice spin systems" (2008). Doctoral Dissertations Available from Proquest. AAI3325255.
https://scholarworks.umass.edu/dissertations/AAI3325255