Tunnel effect for Kramers-Fokker-Planck type operators: return to equilibrium and applications

Details Tunnel effect for Kramers-Fokker-Planck type operators: return to equilibrium and applications Tunnel effect for Kramers-Fokker-Planck type operators: return to equilibrium and applications

2008-01-23

arxiv.org/abs/0801.3615v1

Mathematics

Analysis of PDEs

Scientific paper

In the first part of this work, we consider second order supersymmetric differential operators in the semiclassical limit, including the Kramers-Fokker-Planck operator, such that the exponent of the associated Maxwellian $\phi$ is a Morse function with two local minima and one saddle point. Under suitable additional assumptions of dynamical nature, we establish the long time convergence to the equilibrium for the associated heat semigroup, with the rate given by the first non-vanishing, exponentially small, eigenvalue. In the second part of the paper, we consider the case when the function $\phi$ has precisely one local minimum and one saddle point. We also discuss further examples of supersymmetric operators, including the Witten Laplacian and the infinitesimal generator for the time evolution of a chain of classical anharmonic oscillators.

Affiliated with

Also associated with

No associations

Rating

Tunnel effect for Kramers-Fokker-Planck type operators: return to equilibrium and applications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Tunnel effect for Kramers-Fokker-Planck type operators: return to equilibrium and applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tunnel effect for Kramers-Fokker-Planck type operators: return to equilibrium and applications will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-183904