Abstract
We develop a recursion procedure for solving the generalized Fokker-Planck equation for a system of three interacting one-mode boson fields including the proof of convergence. Approximate formulae for the quantum antinormal characteristic function and the corresponding quasidistribution are obtained for the whole system and as a consequence quantum fluctuations in single fields, correlations among them and various cases of occurrence of the anticorrelation effect are discussed including losses. Initial fields are assumed to be coherent or partly chaotic and it is shown that in some cases the lossy mechanism as well as if some of these fields are chaotic can support the occurrence of the anticorrelation effect. The most important cases are described by the model of the superposition of coherent and chaotic fields although some corrections to this model are also found.
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Peřinová, V., Peřina, J. Generalized Fokker-Planck equation approach to optical parametric processes I. Equations of motion and their solutions. Czech J Phys 28, 1183–1195 (1978). https://doi.org/10.1007/BF01599960
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DOI: https://doi.org/10.1007/BF01599960