Iterative algorithm versus analytic solutions of the parametrically driven dissipative quantum harmonic oscillator

Details Iterative algorithm versus analytic solutions of the parametrically driven dissipative quantum harmonic oscillator Iterative algorithm versus analytic solutions of the parametrically driven dissipative quantum harmonic oscillator

2000-01-31

arxiv.org/abs/cond-mat/0001451v2

Phys. Rev. E 62, 5808 (2000)

Physics

Condensed Matter

15 pages including 11 figures, one reference added, minor typos corrected

Scientific paper

10.1103/PhysRevE.62.5808

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 (QUAPI). 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.

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