  Making use of a simple unitary transformation we change the hamiltonian of a
particle coupled to an one dimensional gas of bosons or fermions to a new form
from which the many body degrees of freedom can be easily traced out. The
effective dynamics of the particle allows us to compute its damping constant in
terms of the reflection coefficient of the interaction potential and the
occupation number of the environmental particles. We apply our results to a
delta repulsive potential.
