The quantum canonical ensemble

Brody, D C and Hughston, L P. 1998. The quantum canonical ensemble. Journal of Mathematical Physics, 39(12), pp. 6502-6508. ISSN 0022-2488 [Article]

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Abstract or Description

The phase space Γ of quantum mechanics can be viewed as the complex projective space CPn endowed with a Kählerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrödinger equation as generating a Hamiltonian dynamics on Γ. 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 Γ-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.

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19 August 1998Accepted
18 November 1998Published Online
December 1998Published

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10 Mar 2022 09:41

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10 Mar 2022 09:45

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Yes, this version has been peer-reviewed.


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