Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. F. O’Connell, Found. Phys. 13, 83 (1983).
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”.
M. Hillery, R. F. O’Connell, M. O. Scully and E. P. Wigner, Phys. Reports 106 (3), 121 (1984).
E. P. Wigner, Phys. Rev. 40, 749 (1932).
R. J. Glauber, Phys. Rev. 131, 2766 (1963); ibid. Phys. Rev. Lett. 10, 84 (1963).
E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963).
K. E. Cahill and R. J. Glauber, Phys. Rev. 177, 1857, 1882 (1968).
P. D. Drummond and C. W. Gardiner, J. Phys. A 13, 2353 (1980); P. D. Drummond, C. W. Gardiner, and D. F. Walls, Phys. Rev. A24, 914 (1981).
P. D. Drummond and C. W. Gardiner, J. Phys. A 13, 2353 (1980); P. D. Drummond, C. W. Gardiner, and D. F. Walls, Phys. Rev. A24, 914 (1981).
K. Husimi, Proc. Phys. Math. Soc. Japan 22, 264 (1940).
R. F. O’Connell and E. P. Wigner, Phys. Lett. 85A, 121 (1981).
N. D. Cartwright, Physica 83A, 210 (1976).
G. S. Agarwal and E. Wolf, Phys. Rev. D2, 2161 (1970); G. S. Agarwal, Phys. Rev. A4, 739 (1971).
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.
Y. Kano, Proc. Phys. Soc. (Japan) 19, 1555 (1964); ibid. J. Math. Phys. 6, If 13 (1965).
J. G. Kirkwood, Phys. Rev. 44, 31 (1933), Eq. (22).
R. F. O’Connell and L. Wang, in preparation.
R. F. O’Connell and E. P. Wigner, Phys. Rev. A, in press.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Plenum Press, New York
About this chapter
Cite this chapter
O’Connell, R.F. (1986). Quantum Distribution Functions in Non-Equilibrium Statistical Mechanics. In: Moore, G.T., Scully, M.O. (eds) Frontiers of Nonequilibrium Statistical Physics. NATO ASI Series, vol 135. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2181-1_5
Download citation
DOI: https://doi.org/10.1007/978-1-4613-2181-1_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-9284-5
Online ISBN: 978-1-4613-2181-1
eBook Packages: Springer Book Archive