SIMULATING A BROWNIAN TYPE OF MOTION - THE RESCALING-VELOCITY APPROACH VERSUS THE LANGEVIN APPROACH

The dynamics of a classical test particle that evolves deterministical ly in a potential field, and whose velocity is then randomized at regu lar intervals of time, is discussed. A limiting procedure for this typ e of Brownian type of motion is given, which results in a motion like that described by the Langevin equation. Exact analytical solutions fo r free and harmonically bound particles are obtained. It is shown that if the time intervals between randomizing events coincide with the pe riod of harmonic oscillations, thermal equilibrium is not reached. For anharmonic background potentials such a resonant behavior also shows up as a slowing down of the relaxation.