Abstract
It is verified that microreversibility conditions for higher order correlation functions for a classical or quantum markovian system are satisfied if they hold for second order correlation functions. The phase space version of the conditions is given. It is found that in this formulation the distribution function and Green's function for a given ordering mix with those for inverse ordering. We display explicitly the terms arising due to non-com-mutativity of operators for the Weyl ordering. Finally the microreversibility conditions are used to calculate the stationary solution of the master equation describingn photon absorption and emission.
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Agarwal, G.S.: Springer Tracts in Modern Physics, Vol. 70, eds. Höhler, G.,et al., appendix C. New York: Springer 1974
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Carmichael, H.J., Walls, D.F.: (to be published) have analysed our condition of microreversibility for quantum systems from a more microscopic stand point
Carmichael, H.J., Walls, D.F.: (to be published and private correspondence) have also obtained a phase space version of our condition
Agarwal, G.S.: Phys. Rev. A1, 1445 (1970)
Haken, H.: in a series of papers (Z. Physik263, 267 (1973);265, 105, 503 (1973),266, 265 (1974)) has discussed the extent to which the constants of motion can be used to obtain the steady state solution. It is interesting to note that his treatment is not restricted to systems obeying detailed balance and is equally valid for classical and quantum systems
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For the case of 2 photon processes, Loudon, R., and Simaan, H.D., (J. Phys. A8, 539 (1975)) appear to be the first to find a constant of motion which can be shown to be equivalent to (28) withn=2
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Agarwal, G.S. Some aspects of microreversibility for open systems. Z Physik B 22, 177–180 (1975). https://doi.org/10.1007/BF01322362
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DOI: https://doi.org/10.1007/BF01322362