Projection operator approach to the Fokker-Planck equation. II. Dichotomic and nonlinear Gaussian noise

Journal Article · Mon Aug 01 04:00:00 EDT 1988 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01019736· OSTI ID:6008535

Faetti, S; Fronzoni, L; Grigolini, P; Palleschi, V; Tropiano, G

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 finite correlation time /tau/. 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 order /tau//sup 1/ and /tau//sup 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 produced perfect agreement with the exact analytical results (dichotomic noise) and to satisfactorily fit the results of analog simulation (nonlinear Gaussian noise).

• Research Organization: Universita' di Pisa (Italy)
• OSTI ID: 6008535
• Journal Information: J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 52:3-4; ISSN JSTPB
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
COMPUTERIZED SIMULATION
CORRECTIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUILIBRIUM
FLUCTUATIONS
FOKKER-PLANCK EQUATION
GAUSSIAN PROCESSES
MAGNETIC FIELDS
MATHEMATICAL OPERATORS
MECHANICS
NOISE
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PROJECTION OPERATORS
SIMULATION
STATISTICAL MECHANICS
STOCHASTIC PROCESSES
TRANSPORT THEORY
VARIATIONS