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Physical Review A

Effect of nonlinear dissipation on quantum-activated rate processes in condensed phases

George R. Haynes, Gregory A. Voth

Published Aug 1, 1992• 20 citations
Publisher

Abstract

A quantum-activated rate process in the presence of a nonlinear dissipative environment is studied with a Feynman path-integral technique. The nonlinear dissipation arises from specific nonlinear couplings between the reaction coordinate and a many-dimensional bath of effective harmonic oscillators. Such coupling results in a nonlinear influence functional for the effective Feynman path integral along the reaction coordinate. Large nonlinear effects on the rate constant are found at low temperatures.

DOI
10.1103/physreva.46.2143

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A quantum-activated rate process in the presence of a nonlinear dissipative environment is studied with a Feynman path-integral technique. The nonlinear dissipation arises from specific nonlinear couplings between the reaction coordinate and a many-dimensional bath of effective harmonic oscillators. Such coupling results in a nonlinear influence functional for the effective Feynman path integral along the reaction coordinate. Large nonlinear effects on the rate constant are found at low temperatures.
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In this thesis the path integral formalism is applied to the calculation of the dynamics of dissipative quantum systems. The time evolution of a system of bilinearly coupled bosonic modes is treated using the real-time path integral technique in coherent-state representation. This method is applied to a damped harmonic oscillator within the Caldeira-Leggett model. In order to get the stationary trajectories the corresponding Lagrangian function is diagonalized and then the path integrals are evaluated by means of the stationary-phase method. The time evolution of the reduced density matrix in the basis of coherent states is given in simple analytic form for weak system-bath coupling, i.e. the so-called rotating-wave terms can be evaluated exactly but the non-rotating-wave terms only in a perturbative manner. The validity range of the rotating-wave approximation is discussed from the viewpoint of spectral equations. In addition, it is shown that systems without initial system-bath correlations can exhibit initial jumps in the population dynamics even for rather weak dissipation. Only with initial correlations the classical trajectories for the system coordinate can be recovered. The path integral formalism in a combined phase-space and coherent-state representation is applied to the problem of curve-crossing dynamics. The system of interest is described by two coupled one-dimensional harmonic potential energy surfaces interacting with a heat bath. The mapping approach is used to rewrite the Lagrangian function of the electronic part of the system. Using the Feynman-Vernon influence-functional method the bath is eliminated whereas the non-Gaussian part of the path integral is treated using the perturbation theory in the small coordinate shift between potential energy surfaces. The vibrational and the population dynamics is considered in a lowest order of the perturbation. The dynamics of a Gaussian wave packet is analyzed along a one-dimensional reaction coordinate. Also the damping rate of coherence in the electronic part of the relevant system is evaluated within the ordinary and variational perturbation theory. The analytic expressions for the rate functions are obtained in the low and high temperature regimes.
Quantum coherence and its destruction (dephasing) by coupling to a dissipative environment plays an important role in time-resolved nonlinear optical response as well as nonadiabatic transitions and tunneling processes in condensed phases. Generating functions of density-matrix elements and multitime coordinate and momentum correlation functions related to these phenomena are calculated using a pathintegral approach by performing functional integration. The dissipative environment is assumed to be an ensemble of harmonic oscillators and is taken into account by using Feynman-Vernon influence functional. Closed-form expressions for generating functions in terms of the bath spectral density are derived. The present theory generalizes earlier calculations of these quantities to arbitrary temperatures, any dependence of the transition coupling on coordinates (non-Condon effects), and arbitrary order in the interstate coupling. Conditions for factorizing the Liouville-space generating functions that allow a reduced description based on the classical Langevin equation are established. Possible applications to four-wave-mixing spectroscopy and nonadiabatic rate processes are discussed.
An effective and flexible numerical scheme is proposed to simulate the dissipative quantum dynamics of a linearized system–bath Hamiltonian. Based on the observation that the Feynman path integrals for a Gaussian bath have a quadratic functional form, the bath average can be performed by directly sampling paths of the discretized harmonic modes and then propagating the system under the influence of quantum Gaussian force. The algorithm is amenable to all known quantum propagation methods and can thus be flexibly applied to study quantum dissipation in the condensed phase. Nontrivial numerical examples based on the spin-boson and damped quantum oscillator models are presented to demonstrate the application of the new algorithm.
The coupling between system and reservoir is considered to be linear in the coordinates of the bath but nonlinear in the system's coordinate. A dissipative threshold is observed at finite temperatures due to nonlinear dissipation. The quantum decay rate of a metastable state including higher-order expanded terms of the coupling form function is proposed, which can be strongly decreased at finite temperatures when the quantum dissipative threshold is added to the saddle point of the potential.