Perturbation calculation for quasi-equilibrium statistical operator

D. N. Zubarev, В. П. Калашников

Sergiy F. Lyagushyn, Alexander I. Sokolovsky

A complex of issues related to using the Peletminsky–Yatsenko model for the study of non-equilibrium processes is investigated. The problems are associated with the inability of performing the calculation of necessary averages when system states are described by a new, wider set of reduced description parameters, in particular, fluctuations. A matter system interacting with a non-equilibrium system of bosons is considered. The substance is described by two reduced description parameters η1 , η2 and calculations with the quasi-equilibrium statistical operator corresponding to these parameters are technically impossible; at the same time, the calculations can be performed with such operator in the case of the only parameter η1 . Overcoming this problem by considering only small values δη2 of the other reduced description parameter is proposed. An exact definition of δη2 is given, and the theory of perturbations by powers δη2 is developed for the calculation of the initial quasi-equilibrium statistical operator with accuracy up to second-order contributions. Since all further averages are calculated only with the named operator including only η1 , the simplified calculation procedure is carried out for it.On this basis, the theory of non-equilibrium processes in the system of two-level emitters interacting with the boson field is developed. The emitter system is described by excitation degree η1 and the value of emitter correlations η2. The system is considered as a system of spins. The mathematically identical Dicke model describing superradiance and Wagner model introduced for the analogous acoustic phenomenon description are studied. The quasi-equilibrium statistical operator calculation is constructed.

Colin J. Thompson, John M. Blatt

Abstract A perturbation method is developed, and is used to obtain approximate expressions for the expectation values of one-particle and two particle operators in the quasi-chemical equilibrium (pair correlation) approximation to statistical mechanics, for the case of non-extreme Bose-Einstein condensation of the correlated pairs. To lowest order, the approximate results reproduce the results obtained previously for the case of extreme Bose-Einstein condensation.

S. Nakajima

S. Piekarski

This paper gives a formulation of perturbation calculus which is useful for the description of coherent states related to the propagation of ultrasonic waves in crystals. This formulation is based on the results of the theory of coherent states, particularly on the properties of the deformation operator. The method of the construction of the initial state, which is used in perturbation calculus, is verified through comparison with the results of the method of the quasi-equilibrium density matrix based on the use of information theory in statistical physics. The method of perturbation calculus which is presented in this paper describes the time dependence of the mean value of any physical quantity for a crystal which undergoes dynamic deformation. This method makes it possible to grasp the dependence of phenomena observed on the phase and amplitude of the initially excited acoustic wave.

S. V. Peletminskiǐ, V. I. Prikhod'ko