Tensor propagator for iterative quantum time evolution of reduced density matrices. II. Numerical methodology

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Abstract
In a recent Letter [Chem. Phys. Lett. 221, 482 (1994)], we demonstrated that the dynamics of reduced density matrices for systems in contact with dissipative harmonic environments can be obtained in an iterative fashion by multiplication of a propagator tensor. The feasibility of iterative procedures in reduced dimension spaces arises from intrinsic features of the dissipative influence functional in Feynman’s path integral formulation of quantum dynamics. Specifically, the continuum of frequencies characteristic of broad condensed phase spectra disrupts phase coherence to a large extent, such that the dynamics of an augmented reduced density tensor becomes Markovian. In a preceding article [J. Chem. Phys. 102, 4600 (1995)] we examined in detail the formal properties of the tensor propagator. In the present paper we show that the tensor propagator can be further decomposed into a product of small rank tensors, resulting in an extremely simple and efficient numerical scheme that scales almost linearly with the dimension of the augmented reduced density tensor. Numerical application to a model electron transfer reaction is presented.

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