The quantum canonical ensemble

The phase space Gamma of quantum mechanics can be viewed as the complex projective space CPn endowed with a Kahlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as generating a Hamiltonian dynamics on Gamma. Based upon the geometric structure of the quantum phase space we introduce the corresponding natural microcanonical and canonical ensembles. The resulting density matrix for the canonical Gamma-ensemble differs from the density matrix of the conventional approach. As an illustration, the results are applied to the case of a spin one-half particle in a heat bath with an applied magnetic field. (C) 1998 American Institute of Physics. [S0022-2488(98)00212-6].