The Quantum Canonical Ensemble

Details The Quantum Canonical Ensemble The Quantum Canonical Ensemble

1997-09-23

arxiv.org/abs/quant-ph/9709048v2

J.Math.Phys. 39 (1998) 6502-6508

Physics

Quantum Physics

8 pages, minor corrections. to appear in JMP vol. 39

Scientific paper

10.1063/1.532661

The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as generating a Hamiltonian dynamics. 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 ensemble differs from 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.

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