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

Thorwart1, Reimann, Hanggi

  • 1Institut fur Physik, Universitat Augsburg, Universitatsstrasse 1, 86135 Augsburg, Germany.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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This study validates a new iterative algorithm for quantum Brownian motion in modulated potentials. The quasi-adiabatic propagator path-integral algorithm accurately predicts particle behavior, showing reliability for complex quantum systems.

Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter theory

Background:

  • Quantum Brownian motion describes a quantum particle interacting with a thermal environment.
  • Understanding particle dynamics in modulated potentials is crucial for quantum technologies.

Purpose of the Study:

  • To evaluate the accuracy of the quasi-adiabatic propagator path-integral algorithm.
  • To compare analytic solutions with numerical results for quantum Brownian motion.

Main Methods:

  • Simulating quantum Brownian motion in a 1D parabolic potential with modulated curvature.
  • Employing the quasi-adiabatic propagator path-integral algorithm.
  • Deriving and comparing analytic expressions for position and momentum variances.

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Main Results:

  • Good agreement was achieved between analytic expressions and the algorithm's results.
  • The algorithm demonstrated reliability across a broad parameter range.
  • The study confirms the algorithm's efficacy for spatially continuous quantum systems.

Conclusions:

  • The quasi-adiabatic propagator path-integral algorithm is a reliable tool for studying quantum Brownian motion.
  • This method is valuable even when analytical solutions are not readily available.
  • The findings support the algorithm's application in complex quantum system analysis.