NLRT formalism for transient stochastic dynamics

doi:10.1016/0378-4371(89)90085-X

Physica A: Statistical Mechanics and its Applications

Volume 156, Issue 2, 1 April 1989, Pages 628-650

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Abstract

The Non-Linear Relaxation Time (NLRT) technique is presented in the framework of a general and systematic formalism for the characterization of the transient evolution of systems described by Langevin equations. Several examples are studied. The theoretical results are compared with numerical and simulation data and also with those obtained via Mean First Passage Time techniques.

References (19)

P. Colet et al.
Phys. Rev. A
(1988)
M. Suzuki
R.L. StratovichR.L. Stratonovich
N.G. Van Kampen
Stochastic Processes in Physics and Chemistry
(1981)
F. Moss et al.
Noise in Nonlinear Dynamical Systems
(1988)
C.W. Gardiner
H. Risken
K Binder
Phys. Rev. B
(1973)
Z. Racz
Phys. Rev. B
(1976)

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NLRT formalism for transient stochastic dynamics

Abstract

Phys. Rev. A

Stochastic Processes in Physics and Chemistry

Noise in Nonlinear Dynamical Systems

Phys. Rev. B

Phys. Rev. B