Tunnel effect for Kramers-Fokker-Planck type operators

Details Tunnel effect for Kramers-Fokker-Planck type operators Tunnel effect for Kramers-Fokker-Planck type operators

2007-03-23

arxiv.org/abs/math/0703684v2

Mathematics

Spectral Theory

77 pages

Scientific paper

10.1007/s00023-008-0355-y

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.

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