Citation
Hardarson, Askell (1988) Doublewell Tunneling via the Feynman-Kac Formula. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/34ks-xy63. https://resolver.caltech.edu/CaltechETD:etd-09062005-152643
Abstract
We discuss asymptotics of the heat kernel [equation; see abstract in scanned thesis for details] and its x-derivatives when T, λ → ∞ and (T/λ) → 0 where H(λ) = - ((Δ/2) + λ²V) and where V is a double well. When the groundstate is localized in both wells for λ 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, E₀(λ) and E₁(λ).
This formula allows us, in principle, always to go beyond the leading order given by [equation; see abstract in scanned thesis for details] where C is the action of a classical instanton.
| Item Type: | Thesis (Dissertation (Ph.D.)) | ||||
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| Subject Keywords: | Mathematics | ||||
| Degree Grantor: | California Institute of Technology | ||||
| Division: | Physics, Mathematics and Astronomy | ||||
| Major Option: | Mathematics | ||||
| Thesis Availability: | Public (worldwide access) | ||||
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| Defense Date: | 14 September 1987 | ||||
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| Record Number: | CaltechETD:etd-09062005-152643 | ||||
| Persistent URL: | https://resolver.caltech.edu/CaltechETD:etd-09062005-152643 | ||||
| DOI: | 10.7907/34ks-xy63 | ||||
| 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: | 16 Apr 2021 22:26 |
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