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Doublewell tunneling via the Feynman-Kac formula


Hardarson, Askell (1988) Doublewell tunneling via the Feynman-Kac formula. Dissertation (Ph.D.), California Institute of Technology.


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):
  • Simon, Barry M.
Thesis Committee:
  • Unknown, Unknown
Defense Date:14 September 1987
Record Number:CaltechETD:etd-09062005-152643
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3352
Deposited By: Imported from ETD-db
Deposited On:12 Sep 2005
Last Modified:26 Dec 2012 02:59

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