We study the quadratic Kramers-Fokker-Planck operator with a constant magnetic field and with a quadratic potential. We describe the exact expression of the norm of the semi-group associated to the operator near the equilibrium. At this level, explicit and accurate estimates of this norm are shown in small and long times as well as uniform-in-time estimates when the magnetic parameter $b$ tends to infinity.
Categories: math.AP math-ph math.DS math.FA math.MP math.OA