A finite-difference implementation of the Caldeira-Leggett master equation

Journal Article · Wed Jan 21 00:00:00 EST 2009 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.3059006· OSTI ID:21255374

Grossmann, Frank; Koch, Werner ^[1]

---

1. Institut fuer Theoretische Physik, Technische Universitaet Dresden, D-01062 Dresden (Germany)

The Caldeira-Leggett master equation for dissipative quantum dynamics has predominantly been implemented in phase space, where it plays the role of a quantum Fokker-Planck equation. Here we demonstrate the feasibility of a pure coordinate space implementation in the case of intermediate damping strength and temperature, for times long enough to observe thermal equilibration. After a thorough numerical investigation of the analytically solvable harmonic oscillator case, a Morse oscillator model is studied. This is a case in which a quantal phase space approach would be difficult to implement and we show how analytical results for thermal averages are reproduced to a surprisingly high degree.

• OSTI ID: 21255374
• Journal Information: Journal of Chemical Physics, Vol. 130, Issue 3; Other Information: DOI: 10.1063/1.3059006; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
FINITE DIFFERENCE METHOD
FOKKER-PLANCK EQUATION
HARMONIC OSCILLATORS
IMPLEMENTATION
MORSE POTENTIAL
OSCILLATORS
PHASE SPACE