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The Journal of Chemical Physics

A Monte Carlo approach for the real time dynamics of tunneling systems in condensed phases

Elizabeth Behrman, Gary A. Jongeward, Peter Guy Wolynes

Published Dec 15, 1983• 87 citations
Publisher

Abstract

A Monte Carlo method for evaluating real time path integrals is proposed. We study two-level tunneling systems coupled to many body environments. A dynamical correlation function for a model of quantum coherence shows a plateau indicative of the localization effects of damping.
DOI
10.1063/1.445732

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A real-time path-integral Monte Carlo approach is developed to study the dynamics in a many-body quantum system coupled to a phonon background until reaching a nonequilibrium stationary state. The approach is based on augmenting an exact reduced equation for the evolution of the system in the interaction picture which is amenable to an efficient path integral (worldline) Monte Carlo approach. Results obtained for a model of inelastic tunneling spectroscopy reveal the applicability of the approach to a wide range of physically important regimes, including high (classical) and low (quantum) temperatures, and weak (perturbative) and strong electron-phonon couplings.
An alternative formulation of the discrete real time coherent state path integral is examined. Following the development of a previous work [T. L. Marchioro II, J. Math Phys. 31, 2935 (1990)] the discrete coherent state action is transformed to second order form. The resulting path integral expression contains an integrand which factors into a Gaussian probability density and an oscillatory term, making the integral directly amenable to Monte Carlo techniques. Several simple examples in one and two spatial dimensions are presented and the possibilities of extending such an approach to general multidimensional systems are discussed.
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A Monte Carlo method for calculating quantum mechanical time correlation functions is presented. In this method the time correlation function is calculated at several values along the pure imaginary axis of the complex time plane such that 0<it<β, where (β)−1 is the temperature of the system. Using the periodicity of the imaginary time correlation function, the real time behavior is inferred by analytic continuation. The method is used to calculate the absorption spectra of two model systems.