Mean-filed theories with mixed states and associated boson expansions

Abstract

A variational derivation of the Liouville-von Neumann equation of quantum-statistical mechanics is presented, in order to formulate mean-field approximations appropriate to mixed states. The Hartree-Fock and the RPA at finite temperatures are particular cases of the general formalism. A thermal boson expansion is defined, which allows us to describe anharmonic motion around a thermal excited state. In a numerical application on the basis of the Lipkin model, temperature-dependent phase transitions are observed.