ISSN:
1572-9613
Keywords:
Langevin equation
;
delta expansion
;
nonlinear
;
perturbation expansion
;
scaling relations
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force with〈f(t)f(t′)〉=2δ(t−t′), andW(x) is of the formgx 1+2δ. The parameterδ is a measure of the nonlinearity of the equation. We show how to obtain the correlation functions〈x(t)f(t′)〉···x(t( n))〉 f as a power series inδ. We obtain three terms in theδ expansion and show how to use Padé approximants to analytically continue the answer in the variableδ. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg andδ.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01057884
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