Effect of colored noise on an overdamped Josephson junction

In this paper my attention is restricted to stochastic differential equatio n in phase function phi (t), describing an overdamped Josephson junction. I accept the RSJ (resistively shunted junction) modeling, when the contact c haracterized by resistance R and critical current I-c is under the action o f a given direct current I and stochastic current source (I) over tilde (i) (<(I) over tilde (t)> = 0): (h) over bar /2eR d phi /dt + I(c)sin phi = I + (I) over tilde (t). (A) In our case the thermal noise is a Gaussian process and obeys the Johnson-N yquistr correlation law C(t) = <(I) over tilde (t)(I) over tilde (0)> = (h) over bar /2 piR integra l (infinity)(-infinity) d omega /2k(B)T) cos omegat (B) The effective Fokker-Planck equation is derived and the current-voltage cha racteristics (CVCs) of the Josephson junction are calculated for weakly col ored noise. In the limit lim((h) over bar -->0) C(t) = 2k(B)T/R delta (t) (B') the well-known results for white noise are recovered. (C) 2001 Elsevier Sci ence B.V. All rights reserved.