Dephasing due to the interaction with chaotic degrees of freedom

We consider the motion of a particle, taking into account its interaction with environmental degrees of freedom. The dephasing time is determined by the nature of the environment, and depends on the particle velocity. Our interest is in the case where the environment consists of few chaotic degrees of freedom. We obtain results for the dephasing time, and compare them with those of the effective-bath approach. The latter approach is based on the conjecture that the environment can be modelled as a collection of infinitely many harmonic oscillators. The work is related to studies of driven systems, quantum irreversibility, and fidelity. The specific model that we consider requires the solution of the problem of a particle-in-a-box with moving wall, whose 1D version is related to the Fermi acceleration problem.