Hardarson, Askell (1988) Doublewell tunneling via the Feynman-Kac formula. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-09062005-152643
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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.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Degree Grantor:||California Institute of Technology|
|Division:||Physics, Mathematics and Astronomy|
|Thesis Availability:||Restricted to Caltech community only|
|Defense Date:||14 September 1987|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||12 Sep 2005|
|Last Modified:||26 Dec 2012 02:59|
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