  We consider an inhomogeneous linear Boltzmann equation, with an external
confining potential. The collision operator is a simple relaxation toward a
local Maxwellian, therefore without diffusion. We prove the exponential time
decay toward the global Maxwellian, with an explicit rate of decay. The methods
are based on hypoelliptic methods transposed here to get spectral information.
They were inspired by former works on the Fokker-Planck equation and the main
feature of this work is that they are relevant although the equation itself has
no regularizing properties.
