The phase space Γ of quantum mechanics can be viewed as the complex projective space 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.
REFERENCES
1.
2.
L. P. Hughston, in Twistor Theory, edited by S. Huggett (Marcel Dekker, New York, 1995).
3.
A. Ashtekar and T. A. Schilling, in On Einstein’s Path, edited by A. Harvey (Springer, Berlin, 1998).
4.
J.
Anandan
and Y.
Aharonov
, Phys. Rev. Lett.
65
, 1697
(1990
).5.
6.
G. C.
Ghirardi
, A.
Rimini
, and T.
Weber
, Phys. Rev. D
34
, 470
(1989
);
This content is only available via PDF.
© 1998 American Institute of Physics.
1998
American Institute of Physics
You do not currently have access to this content.
