Iterative algorithm versus analytic solutions of the parametrically drivendissipative quantum harmonic oscillator

We consider the Brownian motion of a quantum-mechanical particle in a one-d imensional parabolic potential with periodically modulated curvature under the influence of a thermal heat bath. Analytic expressions for the time-dep endent position and momentum variances are compared with results of an iter ative algorithm, the so-called quasiadiabatic propagator path-integral algo rithm. We obtain good agreement over an extended range of parameters for th is spatially continuous quantum system. These findings indicate the reliabi lity of the algorithm also in cases for which analytic results may not be a vailable a priori.