  Understanding mechanisms for energy dissipation from nanoparticles in contact
with large samples is a central problem in describing friction microscopically.
Calculation of the reduced density matrix appears to be the most suitable metho
to study such systems that are coupled to a large environment. In this paper
the time evolution of the reduced density matrix has been evaluated for an
arbitrary system coupled to a heat reservoir. The formalism is then applied to
study the vibrational relaxation following the stick-slip motion of a small
adsorbate on a surface. The frequency dependence of the relaxation time is also
determined.
