A finite-difference implementation of the Caldeira-Leggett master equation.
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.
Grossmann
Frank
F
Institut fur Theoretische Physik, Technische Universitat Dresden, D-01062 Dresden, Germany. frank@physik.tu-dresden.de
Koch
Werner
W
D002623:Chemistry Techniques, Analytical / Q000379:methods; D002627:Chemistry, Physical / Q000379:methods*; D003198:Computer Simulation; D007700:Kinetics; D015233:Models, Statistical; D008962:Models, Theoretical; D009991:Oscillometry; D011789:Quantum Theory; D013696:Temperature