Quantum Distribution Functions in Non-Equilibrium Statistical Mechanics
Quantum distribution functions provide a means of expressing quantum mechanical averages in a form which is very similar to that for classical averages. Also, the Bloch equation for the density matrix for a canonical ensemble is replaced by a classical equation and, turning to dynamics, the von Neumann equation describing the time development of the density matrix is replaced by a classical equation which is similar in form to the Liouville equation but contains exactly the same information as the quantum von Neumann equation.
KeywordsDensity Matrix Wigner Function Canonical Ensemble Liouville Equation Wigner Distribution
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- 2.R. F. O’Connell in Laser Physics, ed. by J. D. Harvey and D. F. Walls (Springer-Verlag, 1983), p. 238. In the third line from the bottom of p. 244 and in the first line of Section 4 on p. 245, the subscript “a” should be replaced by “n”.Google Scholar
- 7.K. E. Cahill and R. J. Glauber, Phys. Rev. 177, 1857, 1882 (1968).Google Scholar
- 14.R. J. Glauber, in Quantum Optics and Electronics, ed. by C. deWitt, A. Blanden, and C. Cohen-Tannoudji ( Gordon and Breach, New York, 1965 ), p. 65.Google Scholar
- 17.R. F. O’Connell and L. Wang, in preparation.Google Scholar
- 18.R. F. O’Connell and E. P. Wigner, Phys. Rev. A, in press.Google Scholar
- 19.See, for example, R. Graham in Quantum Statistics in Optics and Solid- State Physics, Vol. 66 of “Springer Tracts in Modern Physics”, edited by G. Höhler ( Springer-Verlag, New York, 1973 ), p. 80.Google Scholar