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physica status solidi (b)

Towards Fading of Memory in the Generalized Master Equation Theories of Excitation Transfer

Vladislav Čápek, Ilya Rips

Published Feb 1, 1980• 9 citations
Publisher
DOI
10.1002/pssb.2220970238

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Our recent investigation led to the conclusion that there is much agreement among theories of the excitation transfer: the generalized master equation (GME), the Haken-Strobl-Reineker stochastic-Liouville-equation theory, and the Grover-Silbey microscopic theory. Trapping effects influence memory functions entering the GME. Decoupling of the rest of the system from the sink in the nearly coherent regime for large trapping rates changes the form of the pausing-time-distribution functions and probability densities in the continuous-time random-walk method.
Generalized master equations with nonlinear memory functions describing quasiparticle transport on lattices are derived explicitly from the discrete nonlinear Schr\"odinger equation through the application of diagonalizing projection operators. Exact results are presented for dimers, and an approximation scheme is developed for extended systems such as an infinite chain, which treats the nonlinearity exactly and the intersite transfer perturbatively. An apparent connection to the Toda lattice is pointed out. The exact results presented for the dimer include an explicit evaluation of the initial (driving) term in the generalized master equation.
In the framework of the theory of open quantum systems, we derive quantum master equations for the ultrastrong system-bath coupling regime and, more generally, the strong-decoherence regime. In this regime, the strong decoherence is complemented by slow relaxation processes. We use a generalization of the F\"orster and modified Redfield perturbation theories known in the theory of excitation-energy transfer. Also, we show that the mean-force Gibbs state in the corresponding limits is stationary for the derived master equations.