Tunnel effect and symmetries for Kramers–Fokker–Planck type operators

Source abstract

Abstract We study operators of Kramers–Fokker–Planck type in the semiclassical limit, assuming that the exponent of the associated Maxwellian is a Morse function with a finite number n 0 of local minima. Under suitable additional assumptions, we show that the first n 0 eigenvalues are real and exponentially small, and establish the complete semiclassical asymptotics for these eigenvalues.