Effect of colored noise on an overdamped Josephson junction

Abstract

In this paper my attention is restricted to stochastic differential equation in phase function φ(t), describing an overdamped Josephson junction. I accept the RSJ (resistively shunted junction) modeling, when the contact characterized by resistance R and critical current I c is under the action of a given direct current I and stochastic current source I ̃ (t) (〈 I ̃ (t)〉=0) : (A) ℏ 2 eR dφ dt +I c sinφ=I+ I ̃ (t). In our case the thermal noise is a Gaussian process and obeys the Johnson–Nyquistr correlation law (B) C(t)=〈 I ̃ (t) I ̃ (0)〉= ℏ 2πR ∫ −∞ ∞ dω ω coth ℏω 2k BT cosωt. The effective Fokker–Planck equation is derived and the current-voltage characteristics (CVCs) of the Josephson junction are calculated for weakly colored noise. In the limit (B′) lim ℏ→0C(t)= 2k BT R δ(t) the well-known results for white noise are recovered.