Physics – Condensed Matter – Statistical Mechanics
Scientific paper
Oct 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979phrva..20.1628s&link_type=abstract
Physical Review A - General Physics, 3rd Series, vol. 20, Oct. 1979, p. 1628-1647.
Physics
Condensed Matter
Statistical Mechanics
226
Physical Properties, Statistical Mechanics, Stochastic Processes, Chemical Reactions, Dynamic Characteristics, Eigenvalues, Fluctuation Theory, Fokker-Planck Equation, Harmonic Generations, Langevin Formula, Nonlinear Optics, Raman Spectra
Scientific paper
For a large class of nonlinear stochastic processes with pure multiplicative fluctuations the corresponding time-dependent Fokker-Planck-equation is solved exactly by analytic methods. A universal eigenvalue spectrum and the corresponding set of eigenfunctions are obtained in closed form. The eigenvalue spectrum consists of a discrete as well as a continuous part. To emphasize the significance of the model proposed for the description of more-general stochastic processes the authors investigate its stability with respect to the inclusion of weak additive fluctuations. A discussion of the differences in the static as well as the dynamic behavior of multiplicative and additive stochastic processes is given in detail. It is shown explicitly how internal as well as externally imposed fluctuations can lead to multiplicative stochastic processes. The applications of the results to various fields such as nonlinear optics, electronic devices, autocatalytic chemical reactions, and population dynamics are given.
Brand H. H.
Schenzle Axel
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