Strong Coupling Theory for Tunneling and Vibrational Relaxation in Driven Bistable Systems
✍ Scribed by M. Thorwart; M. Grifoni; P. Hänggi
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 498 KB
- Volume
- 293
- Category
- Article
- ISSN
- 0003-4916
No coin nor oath required. For personal study only.
✦ Synopsis
A study of the dynamics of a tunneling particle in a driven bistable potential which is moderately to strongly coupled to a bath is presented. Upon restricting the system dynamics to the Hilbert space spanned by the M lowest energy eigenstates of the bare static potential, a set of coupled non-Markovian master equations for the diagonal elements of the reduced density matrix, within the discrete variable representation, is derived. The resulting dynamics is in good agreement with predictions of ab-initio real-time path integral simulations. Numerous results, analytical as well as numerical, for the quantum relaxation rate and for the asymptotic populations are presented. Our method is particularly convenient to investigate the case of shallow, time-dependent potential barriers and moderate-to-strong damping, where both a semi-classical and a Redfield-type approach are inappropriate. C 2001 Academic Press CONTENTS I. Introduction. A. Experiments. B. Prior theoretical approaches. II. The driven dissipative bistable system. III. The reduced density matrix in the discrete variable representation DVR. A. The Feynman-Vernon influence functional. B. Real-time paths in the DVR basis. C. The population of the left well. D. An example: The symmetric double-doublet system. IV. The generalized non-interacting cluster approximation. V. The generalized master equation in the discrete variable representation. A. General derivation. B. The leading order approximation. C. Comparison with numerical ab-initio path integral simulations. VI. The quantum relaxation rate. A. Markovian approximation. B. The quantum relaxation rate. VII. Results: Quantum relaxation rate and asymptotic populations. A. Absence of external driving. B. The influence of external (time-dependent) driving forces. C. Dependence on the bath parameters. VIII. Conclusions and outlook. Appendixes. A. Scaling to dimensionless quantities. B. The bath correlation function. C. Numerical iteration scheme for solving the generalized master equation. D. Example: A single path subject to dissipation. E. Harmonic well approximation. F. Flow to weak damping.