Michael Thorwart
Tunneling and vibrational relaxation in driven multilevel systems
Supervisor: Prof. Dr. Peter Hänggi [Theoretical physics I]
Date of oral examination: 07/14/2000
142 pages, english , Shaker Verlag, Aachen 2000; ISBN 3-8265-8271-3
In this thesis, dissipative tunneling systems in presence of external forces are studied in terms of the real-time path integral formalism. Starting from a fully microscopic system-bath Hamiltonian the Feynman-Vernon formulation is used as a basis for two major approaches to driven dissipative quantum systems:

In the first part of the thesis, we analyze in detail the numerical quasiadiabatic propagator path integral (QUAPI) method first developed in the group of N. Makri. Its applicability to spatially continuous driven dissipative quantum systems is demonstrated in a benchmark test. Namely, this numerical technique is applied to the problem of the parametrically driven dissipative quantum harmonic oscillator. For an Ohmic bath, analytical results for the position and momentum variances are compared with the numerical results obtained by using QUAPI. A very good agreement is found for weak to intermediate system-bath coupling strengths and intermediate temperatures. Also in the regime of strong system-bath coupling, low temperature and large driving strength, a satisfactory agreement is achieved although the deviations become noticeable. The comparison reveals that the iterative algorithm of QUAPI yields reliable results for driven dissipative spatially continuous quantum systems. This confirmation permits to use the QUAPI technique as a reference method for other approximation schemes.

In the second part of the thesis, an analytical method is developed to describe the dynamics of a driven dissipative multilevel system. The focus thereby lies on the study of the decay of a state initially localized in one (metastable) well of a (driven) double-well potential. The common restriction of the spatially continuous bistable potential to its two lowest energy eigenstates (spin-Boson problem) is released and higher lying energy eigenstates are taken into account. This generalization allows for a considerable extension of the investigated parameter regime. By treating the bath-induced correlations between quantum paths within a generalized non-interacting cluster approximation, a generalized master equation for the diagonal elements of the reduced density matrix is derived. It turns out that the approximation is appropriate in the regime of moderate temperature and/or moderate system-bath coupling. A further simplification of the integro-differential equation leads to a Markovian approximated master equation whose rate coefficients are obtained as closed analytical expressions. By comparing the results of the full generalized master equation, of the Markovian approximated master equation and of the numerical QUAPI-algorithm, we conclude that the analytical approximation permits correct predictions for the decay process out of the initially populated potential well. The rate governing the long-time dynamics of the decay is obtained as the smallest eigenvalue of the matrix of the (time averaged) rate coefficients. The dependence of this quantum decay rate and of the asymptotic population of the metastable well on the various physical parameters is investigated in detail. Several footprints of quantum mechanical effects in the strongly damped tunneling system are identified.