Abstract
Two models for the Freedericksz transition in a fluctuating magnetic field are considered: one is based on a dichotomic and the other on a nonlinear Gaussian noise. Both noises are characterized by a finite correlation timeτ. It is shown that the linear response assumption leading to the “best Fokker-Planck approximation” in the dichotomic and nonlinear Gaussian cases can be trusted only up to the orderτ 1 andτ 0, respectively. The role of the corrections to the linear response approximation is discussed and it is shown how to replace the non-Fokker-Planck terms stemming from these corrections with equivalent terms of standard type. This technique is shown to produce perfect agreement with the exact analytical results (dichotomic noise) and to satisfactorily fit the results of analog simulation (nonlinear Gaussian noise).
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Faetti, S., Fronzoni, L., Grigolini, P. et al. The projection operator approach to the Fokker-Planck equation. II. Dichotomic and nonlinear Gaussian noise. J Stat Phys 52, 979–1003 (1988). https://doi.org/10.1007/BF01019736
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DOI: https://doi.org/10.1007/BF01019736