Tunneling Systems in Condensed Phases: Quantum Dynamical Monte Carlo and Analytical Theories
Behrman, Elizabeth Colden
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https://hdl.handle.net/2142/77310
Description
Title
Tunneling Systems in Condensed Phases: Quantum Dynamical Monte Carlo and Analytical Theories
Author(s)
Behrman, Elizabeth Colden
Issue Date
1985
Department of Study
Chemical Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Chemistry, Physical
Language
eng
Abstract
A Monte Carlo method for the evaluation of real time path integrals at finite temperatures is proposed. The technique is applied to two level tunneling systems coupled to many body environments, models for electron transfer and for the quantum coherence phenomenon in Josephson junctions. A dynamical correlation function for the latter shows a plateau indicative of the localization effects of damping.
An optimized random phase approximation is derived from an expansion of the free energy in terms of the generating functional. The theory is applied to a two level system coupled to a Gaussian bath. Short time behavior and long time averages of correlation functions are reproduced well.
A general method of renormalization of influence functional bonds for the Monte Carlo calculations is examined. It was hoped that the scheme would reduce significantly the problem of phase cancellation that is the major limitation on the real time Monte Carlo method. Unfortunately the algorithms did not seem to improve convergence to any great extent.
Using a complex time correlation function that greatly improves the convergence properties of the Monte Carlo method, results for the two level system coupled to a dissipative bath are presented. Defects and advantages of various analytical theories are highlighted by comparison to the (statistically) exact results of the Monte Carlo.
Equations are derived for influence functional bonds due to a damped harmonic bath whose initial and/or final points are fixed, a possible importance sampling route for the calculation of rate constants.
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