In the framework of quantum statistical mechanics, based on the parametric nonadditive entropy of Tsallis, related to the density matrix, a dynamic theory of linear response of nonextensive quasi-equilibrium many-body systems to an external time-dependent perturbation is developed. In this paper, for the nonextensive quantum system proposed a modification of the Kubo theory developed in the framework of classical quantum mechanics. The construction of the microscopic theory of the linear reaction was carried out on the basis of the generalized canonical type of the density matrix, obtained by maximizing the Tsallis quantum entropy by averaging the observed values over the escort distribution. The generalized expressions for the admittance and the response function are presented, which describe the linear dependence of the system (with a time independent Hamiltonian) on a weak external mechanical action. The symmetry property for the relaxation function under time reversal and the Onsager reciprocity relation for generalized susceptibility are discussed. It is shown that these properties known in classical quantum statistics also remain valid for anomalous systems.

quantum nonextensive statistics, generalized canonical distribution of the density matrix, linear reaction of the system

Mathematical modelling in actual problems of science and technics

Kolesnichenko Aleksandr Vladimirovich,  ,  orcid.org/0000-0003-1416-5634,  KIAM RAS