title: Iterative algorithm versus analytic solutions of the parametrically driven dissipative quantum harmonic oscillator
abstract: We consider the Brownian motion of a quantum-mechanical particle in a one-dimensional parabolic potential with periodically modulated curvature under the influence of a thermal heat bath. Analytic expressions for the time-dependent position and momentum variances are compared with results of an iterative algorithm, the so-called quasiadiabatic propagator path-integral algorithm. We obtain good agreement over an extended range of parameters for this spatially continuous quantum system. These findings indicate the reliability of the algorithm also in cases for which analytic results may not be available a priori.
authors.affiliation: Institut fur Physik, Universitat Augsburg, Universitatsstrasse 1, 86135 Augsburg, Germany.
authors.initials: M
authors.lastname: Thorwart
authors.initials: P
authors.lastname: Reimann
authors.initials: P
authors.lastname: Hanggi