An otherwise free classical particle moving through an extended spatially
homogeneous medium with which it may exchange energy and momentum will undergo
a frictional drag force in the direction opposite to its velocity with a
magnitude which is typically proportional to a power of its speed. We study
here the quantum equivalent of a classical Hamiltonian model for this friction
phenomenon that was proposed in [11]. More precisely, we study the spectral
properties of the quantum Hamiltonian and compare the quantum and classical
situations. Under suitable conditions on the infrared behaviour of the model,
we prove that the Hamiltonian at fixed total momentum has no ground state
except when the total momentum vanishes, and that its spectrum is otherwise
absolutely continuous.Comment: 40 page
