Abstract.
We consider operators of Kramers–Fokker–Planck type in the semi-classical limit such that the exponent of the associated Maxwellian is a Morse function with two local minima and a saddle point. Under suitable additional assumptions we establish the complete asymptotics of the exponentially small splitting between the first two eigenvalues.
Résumé.
On considère des opérateurs du type de Kramers–Fokker–Planck dans la limite semi-classique tels que l’exposant du maxwellien associé soit une fonction de Morse avec deux minima et un point selle. Sous des hypothèses supplémentaires convenables on établit un développement asymptotique complet de l’écart exponentiellement petit entre les deux premières valeurs propres.
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Communicated by Christian Gérard.
Submitted: April 3, 2007. Accepted: October 4, 2007.
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Hérau, F., Hitrik, M. & Sjöstrand, J. Tunnel Effect for Kramers–Fokker–Planck Type Operators. Ann. Henri Poincaré 9, 209–274 (2008). https://doi.org/10.1007/s00023-008-0355-y
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DOI: https://doi.org/10.1007/s00023-008-0355-y