Abstract:
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 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.
Keywords:quantum nonextensive statistics, generalized canonical distribution of the density matrix, linear reaction of the system.
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