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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. doi:10.7907/34ks-xy63.


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.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Simon, Barry M.
Thesis Committee:
  • Simon, Barry M. (chair)
  • Luxemburg, W. A. J.
  • Katok, Anatole
  • Koonin, Steven E.
Defense Date:14 September 1987
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
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:16 Apr 2021 22:26

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