Effective-Eigenvalue Approach to the Nonlinear Langevin Equation for the Brownian motion in a Tilted Periodic Potential: Application to the Josephson Tunneling Junction
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Date
1993
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Abstract
The concept of the effective eigenvalue appears to have been originally
introduced into the study of relaxation problems in statistical physics by
Leontovich.’ It was later developed and applied (sometimes implicitly) to
a variety of stochastic problems in laser
polar fluids,’ polymers,8 nematic liquid crystals? lo etc. In the present
context, namely the theory of the Brownian motion, the method constitutes
a truncation procedure which allows one using simple assumptions to
obtain closed-form approximations to the solution of certain infinite hierarchies
of differential-difference equations in the time variables. These
magnetic domains,
equations govern the time behavior of the statistical averages characterizing
the relaxation of nonlinear stochastic systems. Thus, their solution is
needed to calculate observable quantities such as the relaxation times and
dynamic susceptibilities of the system.
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Citation
Coffey, W.T., Kalmykov, Y.P. and Massawe, E.S., 1993. Effective-eigenvalue approach to the nonlinear Langevin equation for the Brownian motion in a tilted periodic potential: Application to the Josephson tunneling junction. Physical Review E, 48(1), p.77.