TREATMENT OF INELASTIC-COLLISIONS OF A PARTICLE WITH A QUANTUM HARMONIC-OSCILLATOR BY DENSITY-MATRIX EVOLUTION

A density matrix evolution (DME) method (Berendsen, H. J. C., and Mavri, J., 1993, J. phys. Chem., 97, 13464) to simulate the dynamics of quantum systems embedded in a classical environment is applied to study the inelastic collisions of a classical particle with a five level quantum harmonic oscillator. The results are compared with the exact quantum calculations of Secrest, D., and Johnson, B. R., 1966, J. chem. Phys., 45, 4556, and with the results of classical mechanics. The DME results are between the results of the full quantum treatment and classical mechanics but closer to the latter. Furthermore, we demonstrate the time reversibility of the DME equations of motion and discuss the importance for the time reversibility of the quantum phase described by the off-diagonal elements of the density matrix.