# Taking into account the influence of correlations on the system dynamics in the reduced description method

## DOI:

https://doi.org/10.15421/332302## Keywords:

reduced description method, small parameter, Peltminskii–Yatsenko model, non-equilibrium system of bosons, two-level emitters, Dicke model, Wagner model with tunneling## Abstract

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 η_{1} , η_{2} 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 η_{1} . Overcoming this problem by considering only small values δη_{2} of the other reduced description parameter is proposed. An exact definition of δη_{2} is given, and the theory of perturbations by powers δη_{2} 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 η_{1} , 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 η_{1} and the value of emitter correlations η_{2}. 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.