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Type of Document	Dissertation
Author	Hardarson, Askell
URN	etd-09062005-152643
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-09062005-152643
Title	Doublewell tunneling via the Feynman-Kac formula
Degree	PhD
Option	Mathematics
Advisory Committee	Advisor Name Title Barry Simon Committee Chair
Keywords	none
Date of Defense	1987-09-14
Availability	restricted
Abstract NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. We discuss asymptotics of the heat kernel [...] and its x-derivatives when [...], [...] and [...] where [...] = [...] and where V is a double well. When the groundstate is localized in both wells for [lambda] large we derive, by the Feynman-Kac formula, W.K.B. expansions of the groundstate, the first excited state and their gradients. As a consequence we get a general asymptotic formula for the splitting of the two lowest eigenvalues, [...] and [...]. This formula allows us, in principle, always to go beyond the leading order given by [...] where C is the action of a classical instanton.
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