Abstract
We consider classical systems described by a Fokker-Planck equation or a generalized Fokker-Planck equation and quantum systems described by a density matrix equation or by a generalized Fokker-Planck equation using the principle of quantum classical correspondence. We split the corresponding operators of the equation of motion into a part which refers to the proper system and another one which describes the coupling of the proper system to the external world (reservoirs). We demonstrate that by use of conservation laws, referring to the proper systems, exact relations hold for certain moments, valid for all temperatures and coupling constants of the reservoirs. Using the concepts of a previous paper we describe then a perturbation theoretical approach which allows in a simple manner to determine a number of important correlation functions (moments of the total system). The time dependent case is briefly discussed. The applicability and usefulness of the present procedure is demonstrated by the example of the single-mode laser yielding e.g. expressions for the atom-field correlation.
Similar content being viewed by others
References
See e.g. the articles by Schlögl, F. C., Kubo, R., Kawasaki, K., Mori, H., Grossmann, S., Graham, R., Thomas, H., Landauer, R., Woo, J. W. F., Prigogine, I., Lefever, R., Kerner, E. H., Montroll, E. W., West, B. J., Fröhlich, H., Wagner, M., Weidlich, W., and others: In: Synergetics, ed. H. Haken. Stuttgart: Teubner 1973, where many further references may be found
Haken, H.: Z. Physik263, 267 (1973)
Haken, H.: Encyclopedia of physics, XXV/2c. Berlin-Heidelberg-New York: Springer 1970
Haken, H., Wöhrstein, H. G.: Optics Comm. in press (1973)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Haken, H. Correlations in classical and quantum systems far from thermal equilibrium. Z. Physik 265, 503–510 (1973). https://doi.org/10.1007/BF01391805
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01391805