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Regular and Chaotic Dynamics, 2006, Volume 11, Issue 2, Pages 167–180
DOI: https://doi.org/10.1070/RD2006v011n02ABEH000343 (Mi rcd666) 		 
This article is cited in 14 scientific papers (total in 14 papers)

On the 70th birthday of L.P. Shilnikov

Unstable closed trajectories, librations and splitting of the lowest eigenvalues in quantum double well problem

J. Brüeninga, S. Yu. Dobrokhotovb, E. S. Semenovb

a Institut für Mathematik, Humboldt Universität zu Berlin Rudower Chaussee 25, 12489 Berlin, Germany
b Institute for Problems in Mechanics, RAS, pr. Vernadskogo 101, 117526 Moscow, Russia
Citations (14)
DOI: https://doi.org/10.1070/RD2006v011n02ABEH000343
Abstract: We discuss the structure of asymptotic splitting formula for the lowest eigenvalues of multidimensional quantum double well problem. We show that the change of instanton by closed unstable trajectory of appropriate Hamiltonian system gives more natural and simpler preexponential factor (amplitude) in splitting formula. The projection of this trajectories onto configuration space are well know librations in classical mechanics.
Keywords: quantum double well problem, librations, splitting value, tunneling effect, normal forms, complex phase space.
Received: 26.09.2005
Accepted: 11.11.2005
Bibliographic databases:
Document Type: Article
MSC: 81Q20, 81S10, 53D12, 37J45
Language: English
Citation: J. Brüening, S. Yu. Dobrokhotov, E. S. Semenov, “Unstable closed trajectories, librations and splitting of the lowest eigenvalues in quantum double well problem”, Regul. Chaotic Dyn., 11:2 (2006), 167–180
Citation in format AMSBIB
\Bibitem{BruDobSem06}
\by J. Br\"uening, S. Yu. Dobrokhotov, E. S. Semenov
\paper Unstable closed trajectories, librations and splitting of the lowest eigenvalues in quantum double well problem
\jour Regul. Chaotic Dyn.
\yr 2006
\vol 11
\issue 2
\pages 167--180
\mathnet{http://mi.mathnet.ru/rcd666}
\crossref{https://doi.org/10.1070/RD2006v011n02ABEH000343}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2245075}
\zmath{https://zbmath.org/?q=an:1164.81312}
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    • This publication is cited in the following 14 articles:
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