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Journal of the Physical Society of Japan

Theory of Exchange Dephasing. II. Quantum Theory of Random Frequency Modulation

Fumiaki Shibata, Toshihico Arimitsu, Yoko Hamano

Published Jul 1, 1982• 11 citations
Publisher

Abstract

With the use of the basic equation derived in the previous paper, the exchange dephasing phenomena are examined by a quantum theory of random frequency modulation. Under a certain circumstance a quantal stochastic process is shown to be the Gaussian-Markoffian process. Time-correlation function and power spectrum are obtained: Temperature dependence of frequency shift and width of line shape is also determined.

DOI
10.1143/jpsj.51.2075

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With the use of the basic equation derived in the previous paper, the exchange dephasing phenomena are examined by a quantum theory of random frequency modulation. Under a certain circumstance a quantal stochastic process is shown to be the Gaussian-Markoffian process. Time-correlation function and power spectrum are obtained: Temperature dependence of frequency shift and width of line shape is also determined.
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It is shown that the Heisenberg equation of motion can be transformed exactly into the reduced form dA(t)/dt = [ iΩ-∫t0ψ(s)ds] ·A(t)+g(t), where A(t) is an arbitrary column vector of dynamical variables, Ω is a frequency matrix determining collective oscillations, and g(t) is a fluctuating force. ψ(t) differs from the memory function and is related to the time-correlation function of g(t) by ψ(t) = (g(t), g*(0))·(A(t), A*(0))-1. This equation of motion is shown to give a statistical-mechanical theory of random frequency modulations, including Kubo's theory of the stochastic Liouville equation, and to lead to a new theory of generalized Brownian motions which complements a memory-function theory given by Mori.
A stochastic approach to the quantum dynamics randomly modulated in time by a discrete state non-Markovian noise, which possesses an arbitrary nonexponential distribution of the residence times, is developed. The formally exact expression for the Laplace-transformed quantum propagator averaged over the stationary realizations of such N -state non-Markovian noise is obtained. The theory possesses a wide range of applications. It includes some previous Markovian and non-Markovian theories as particular cases. In the context of the stochastic theory of spectral line shape and relaxation, the developed approach presents a non-Markovian generalization of the Kubo-Anderson theory of sudden modulation. In particular, the exact analytical expression is derived for the spectral line shape of optical transitions described by a Kubo oscillator with randomly modulated frequency which undergoes jumplike non-Markovian fluctuations in time.
We present a theoretical approach to describe the dynamics of a system induced by stochastic couplings and undergoing dephasing processes. We consider a model frequently encountered in the study of non-radiative transitions in molecular systems, the case of two configurations stochastically coupled. In this model, we use a system whose excited radiant state is coupled stochastically to a non-radiant state of a lower electronic configuration. We show the line shape for stochastic non-diagonal perturbations to remain Lorentzian. This result is different from the case of frequency modulation where a transition from a Gaussian to a Lorentzian line shape can be observed.