Quantum statistical hierarchy equation in nonequilibrium systems
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An extension is given for the Fourier expansion method with the contraction technique, which was introduced by Balescu for quantum statistical systems. This is attained by introducing a diagrammatic method with a concept of moving contraction. Then the hierarchy equation for the Contracted Fourier coefficient of the Wigner distribution function is obtained. As an application, a generalized master equation involvingn-body collision effects and quantum statistical effects is also derived.
Key wordsWigner distribution function Fourier expansion method quantum statistical hierarchy equation diagrammatic method movable and unmovable contractions
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- 1.I. Prigogine and R. Balescu,Physica 25:281 (1959);25:302 (1959);26:145 (1960); I. Prigogine,Non-Equilibrium Statistical Mechanics, Interscience, New York (1962).Google Scholar
- 2.R. Balescu,Statistical Mechanics of Charged Particles, Interscience, New York (1963).Google Scholar
- 3.L. Van Hove,Physica 21:517 (1955);23:441 (1957).Google Scholar
- 4.N. N. Bogoliubov,Lectures on Quantum Statistics, Vol. 1, L. Kline and S. Glass, eds., Gordon and Breach, New York (1967).Google Scholar
- 5.J. G. Kirkwood,J. Chem. Phys. 19:1173 (1951).Google Scholar
- 6.I. Prigogine and S. Ono,Physica 25:171 (1959).Google Scholar
- 7.F. Henin, P. Résibois, and F. Andrews,J. Math. Phys. 2:68 (1961).Google Scholar
- 8.I. Prigogine, C. George, and F. Henin,Physica 45:418 (1969).Google Scholar
- 9.R. Balescu,Physica 62:485 (1972).Google Scholar