Novel perturbation expansion for the Langevin equation |
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| Authors: | Carl Bender Fred Cooper L M Simmons Jr Pinaki Roy Greg Kilcup |
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| Institution: | (1) Physics Department, Washington University, 63101 St. Louis, Missouri;(2) Theoretical Division, Los Alamos National Laboratory, 87545 Los Alamos, New Mexico;(3) Santa Fe Institute, 87501 Santa Fe, New Mexico;(4) Electronics Unit, India Statistical Institute, 700035 Calcutta, India;(5) Department of Physics, Ohio State University, 43210 Columbus, Ohio |
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| 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 ) =2 (t–t), andW(x) is of the formgx
1+2. The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t(
n))
f
as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and. |
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| Keywords: | Langevin equation delta expansion nonlinear perturbation expansion scaling relations |
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