Citation
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
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.
| Item Type: | Thesis (Dissertation (Ph.D.)) |
|---|---|
| Degree Grantor: | California Institute of Technology |
| Division: | Physics, Mathematics and Astronomy |
| Major Option: | Mathematics |
| Thesis Availability: | Restricted to Caltech community only |
| Research Advisor(s): |
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| Thesis Committee: |
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| Defense Date: | 14 September 1987 |
| Record Number: | CaltechETD:etd-09062005-152643 |
| Persistent URL: | http://resolver.caltech.edu/CaltechETD:etd-09062005-152643 |
| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 3352 |
| Collection: | CaltechTHESIS |
| Deposited By: | Imported from ETD-db |
| Deposited On: | 12 Sep 2005 |
| Last Modified: | 26 Dec 2012 02:59 |
Thesis Files
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