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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Dissipative transfer of a quantum particle in a dimer with random fluctuating intersite matrix element

Igor Goychuk, Elmar G. Petrov, Volkhard May

Published Apr 1, 1995• 17 citations
Publisher

Abstract

Kinetic equations of the quantum particle motion in a symmetric dimer are studied for the case of fluctuating site energies and a fluctuating intersite coupling matrix element. Modulations of the site energies are incorporated via quantum fluctuations of a thermal bath whereas the fluctuations of the intersite coupling are taken into account by a stochastic description. In contrast to the quantum fluctuations which are considered in the weak coupling limit, the stochastic fluctuations are included in an exact manner. The exact solution of the averaged kinetic equations are obtained in the case of an Ohmic thermal bath with a white noise spectrum and dichotomous fluctuations of the intersite coupling.

DOI
10.1103/physreve.51.2982

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Kinetic equations of the quantum particle motion in a symmetric dimer are studied for the case of fluctuating site energies and a fluctuating intersite coupling matrix element. Modulations of the site energies are incorporated via quantum fluctuations of a thermal bath whereas the fluctuations of the intersite coupling are taken into account by a stochastic description. In contrast to the quantum fluctuations which are considered in the weak coupling limit, the stochastic fluctuations are included in an exact manner. The exact solution of the averaged kinetic equations are obtained in the case of an Ohmic thermal bath with a white noise spectrum and dichotomous fluctuations of the intersite coupling.
The nonequilibrium density matrix technique is utilized to study the incoherent transfer of a quantum particle coupled to a fluctuating environment. The dynamics of the environment is assumed to split into two different types of molecular motions. The first type is associated with low-amplitude vibrations forming a thermal bath (TB). High-amplitude displacements of separated molecular groups define the second type and create stochastic fields for acting on the transferred particle. Specifying the TB by a set of harmonic oscillators and the stochastic fields by a dichotomic process averaged kinetic equations were derived. These equations enable us to construct a rate constants expressions and to find the steady-state populations for a quantum particle. Regimes of enhanced or reduced particle transfer are discussed in detail in relation to the characteristics of the stochastic field and the TB. \textcopyright{} 1996 The American Physical Society.
We obtain kinetic equations for the stochastically averaged reduced density matrix of a quantum system driven by a dichotomous Markovian process and weakly coupled to a quantum thermal bath. These kinetic equations are exact in arbitrary dichotomous perturbation and provide a unified description of both small and large correlation time limits, along with an intermediate case. As an example, the problem of a dissipative two-level system with a dichotomically modulated difference in eigenergies is considered.
The transport of a quantum particle in a dimer is investigated for the case in which the influence of phonons from different branches is modeled by a dichotomic stochastic process with exponentially decaying correlations. For physical reasons, these processes might be correlated. An exact equation for the correlations between matrix elements of the density operator and both stochastic processes is constructed, and eigenvalues of the corresponding matrix are found numerically. Correlations between the noises reduce the range of incoherent transport. Various criteria for distinguishing between coherent and incoherent motion are also discussed.
The methods of nonequilibrium density-matrix and coarse-temporal conception are used to obtain the kinetic equation for the parameters ${\ensuremath{\gamma}}_{\mathit{n}\mathit{m}}$(t)=Sp[\ensuremath{\rho}^(t)\ensuremath{\Vert}n〉〈m\ensuremath{\Vert}] of a quantum-dynamic system (QDS) interacting with a thermal bath and external stochastic field. It is important that the stochastic field is taken exactly into consideration. For diagonal QDS parameters ${\ensuremath{\gamma}}_{\mathit{n}\mathit{n}}$(t) this equation is reduced to the generalized Pauli equation (GPE) with stochastic time-dependent coefficients wnm{\mathit{w}}_{\mathit{n}\mathit{m}}wnm​(t). Special attention is given to the procedure of averaging over stochastic processes. It is shown that after averaging over energy fluctuations affected by the stochastic field, in the first cumulant approximation in terms of stochastic processes wnm{\mathit{w}}_{\mathit{n}\mathit{m}}wnm​(t), the GPE is transformed to the Pauli equation for the QDS state population Pn{\mathit{P}}_{\mathit{n}}Pn​(t)=〈${\ensuremath{\gamma}}_{\mathit{n}\mathit{n}}$(t)〉f{\mathrm{〉}}_{\mathit{f}}〉f​. As an example, the relaxation behavior of a two-level system interacting with a dichotomous field (dichotomous Markovian process of kangaroo type) and a harmonic oscillator coupled with a thermal bath is considered. It is shown that the probability of relaxation transitions between energy levels may be changed by several orders of magnitude under the influence of the dichotomous field.
A master equation for a quantum system coupled to a heat bath with stochastically fluctuating energy levels is derived by making use of the ensemble averaging and the averaging with respect to a stochastic process in the bath. Relaxation terms are determined in the Born approximation with respect to the system-bath interaction and the damping parameters related to a relaxation kernel are specified. In parallel with the spectral strength of the bath, the damping parameters determine the transient times for the Markovian description creating the physical origin of the slippage [A. Suarez, R. Sibey, and I. Oppenheim, J. Chem. Phys. 97, 5101 (1992)]. The influence of energy fluctuations of the bath is analyzed for a two-level system including the solution of the corresponding non-Markovian equation for the level population difference. The conditions for the formation of Boltzmann's thermal ratio between steady-state populations are evaluated as well.