  In this paper, we consider the quantum version of the hamiltonian model
describing friction introduced in [BDB]. This model consists of a particle
which interacts with a bosonic reservoir representing a homogeneous medium
through which the particle moves. We show that if the particle is confined,
then the Hamiltonian admits a ground state if and only if a suitable infrared
condition is satisfied. The latter is violated in the case of linear friction,
but satisfied when the friction force is proportional to a higher power of the
particle speed.
