Quantum distribution functions in non-equilibrium statistical mechanics
As we have emphasized in previous investigations of this question, the optimum approach to the problem is via the use of characteristic functions, which are nothing more than Fourier transforms of distribution distributions. The next step is to write P/sub w/(q,p) in terms of the complex variable ..cap alpha... Then we obtain relationships between the various distribution functions, which are readily converted into relationships between the distribution functions, either in q-p or ..cap alpha.. language. For simplicity, we treat a one-dimensional system in a pure state since the case of a mixture in multi-dimensions presents no essential complications. Since the touchstone of our considerations is the Wigner distribution, we write down its properties. We then summarize the properties of the generalized distribution functions of the Cahill-Glauber class and their relation to the Wigner distribution. In addition, we discuss the Husimi (smoothed) distribution function and point out its exact equivalence with the anti-normal distribution. We discuss the Glauber-Sudarshan P (..cap alpha..) function as well as the Q(..cap alpha..) function and also the relation between them and P/sub w/. Then we show that the Q(..cap alpha..), Husimi and anti-normal distributions are identical to each other and, similarly, the Glauber-Sudarshan and normal distributions are identical. Finally, we introduce a new class of generalized distribution functions, with emphasis on two particular cases of same viz., the standard of anti-standard distributions, and we also demonstrate the equivalence of the latter to the Kirkwood distribution. 19 refs.
- Research Organization:
- Louisiana State Univ., Baton Rouge (USA). Dept. of Physics and Astronomy
- DOE Contract Number:
- AS05-79ER10459; FG05-84ER45135
- OSTI ID:
- 5259578
- Report Number(s):
- DOE/ER/45135-12; CONF-8406194-4; ON: DE85016841
- Resource Relation:
- Conference: NATO advanced study institute on nonequilibrium quantum statistical mechanics, Santa Fe, NM, USA, 3 Jun 1984
- Country of Publication:
- United States
- Language:
- English
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