Study of the Kramers–Fokker–Planck quadratic operator with a constant magnetic field

Abstract

We study the quadratic Kramers–Fokker–Planck operator with a constant magnetic field and a quadratic potential. We describe the exact expression of the norm of the semi-group associated with the operator near the equilibrium. At this level, explicit and accurate estimates of this norm are shown in small and long times and uniform-in-time estimates are shown when the magnetic parameter b tends to infinity.