The aim of this paper is to provide better understanding of a few approaches that have been proposed for treating nonequilibrium (time-dependent) processes in statistical mechanics with the emphasis on the interrelation between theories. The ensemble method, as it was formulated by Gibbs, has great generality and broad applicability to equilibrium statistical mechanics. Different macroscopic environmental constraints lead to different types of ensembles, with particular statistical characteristics. In the present work, the statistical theory of nonequilibrium processes which is based on nonequilibrium ensemble formalism is discussed. We also outline the reasoning leading to some other useful approaches to the description of the irreversible processes. The kinetic approach to dynamic many-body problems, which is important from the point of view of the fundamental theory of irreversibility, is alluded to. Appropriate references are made to papers dealing with similar problems arising in other fields. The em...

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Theory of transport processes and the method of the nonequilibrium statistical operator

From four non-stochastic rigorous theories leading to a set of equations for site-diagonal as well as site off-diagonal elements of the electron (carrier) density matrix (Time-Convolution Generalized Master Equation, Mori theory, Time-Convolutionless Generalized Master Equation and Tokuyama-Mori), the first two (time nonlocal) approaches were recently found to be disabled in the second order in the carrier-bath coupling. On the other hand, the latter two (time local) theories are argued here to lead, in the above order and any electronic system with a site-local coupling to bath, to completely identical and physically fully acceptable equations. The theory is applied to a periodic chain and asymmetric dimer. It is shown that, irrespective of problems with introducing γmn or γmn(m≠n) Haken-Strobl-Reineker parameters, the usual transition from the non-activated to activated (Arrhenius-type) ‘up-and-down’ asymmetric Marcus long-time reaction kinetics is obtained. The usual long-time markovian description of the population kinetics assumed in the standard theory is, however, found to be unjustified.

Carrier transfer in inhomogeneous media

A new method for the description of simultaneous creation, annihilation, propagation and relaxation of excitations in exciton (electron) systems interacting with a phonon bath and an ultrashort quantum optical pulse is developed on the basis of generalized master equations derived by using a time-dependent projector. It is shown, that standard theories starting from an already created excitation at a given place, without any off-diagonal elements of the exciton density matrix, have a very limited area of application because off-diagonal elements are generally nonzero once the excited pulse switches off. Derived equations also describe the influence of quantum statistics of the pulse.

Dynamics of excitations in molecular condensates under the influence of an ultrashort pulse

Interplay of simultaneous creation, annihilation, propagation, and relaxation of an excitation in molecular condensates interacting with an ultrashort quantum optical pulse is studied in general and specialized to a dimer. A microscopic model appropriate for such systems (with a strong exciton–phonon coupling) is presented. It also incorporates effects of (quantum) noise in the optical field. A variety of new features in the initial stage of excitation dynamics (when it is being created) is revealed; a strong influence of the coherent excitation propagation on the processes of excitation creation and annihilation in a molecule strongly interacting with phonons is the most remarkable one.

Interplay of creation, propagation, and relaxation of an excitation in a dimer

Generalized master equations describing an exciton (electron) system interacting with a phonon bath and an ultrashort quantum optical pulse are derived. They are considerably simpler than those derived earlier although they are able to describe the interplay of creation, annihilation, propagation and relaxation of an excitation in its full complexity. Their range of validity is limited to smaller values of the excitation and to a weaker exciton-phonon coupling.

Dynamics of excitations in molecular condensates

A trick permitting to apply generalized master equation (GME) theory together with canonical transformation but quantities of interest (single-particle density matrix) remaining untransformed is applied to the time-convolutionless GME approach for carriers interacting with phonons by a local linear coupling. In contrast with time convolution theories (Mori, time-convolution GME), it is found that the second-order perturbational approach in the above coupling is already able to yield a loss of coherence of carrier propagation with increasing time as well as a proper asymptotic state at any temperature. Moreover, dependence on the degree of the initial polaron cloud formation is shown, as expected but again in contrast with the above theories, to disappear explicitly after a short period of the polaron cloud reconstruction from equations determining the time development of the single-particle density matrix. A prediction on the Weber effect and charge-carrier generation process in narrow band materials is given. Correspondence with a recent generalization of the Haken-Strobl-Reineker model is found.

V. Čápek

Papers

Interplay of exciton or electron transfer and relaxation