Effect of colored noise on an overdamped Josephson junction Original Research Article

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 Ic is under the action of a given direct current I and stochastic current source Ĩ(t) (〈Ĩ(t)〉=0): (A)ℏ2eRdφdt+Ic sinφ=I+Ĩ(t). In our case the thermal noise is a Gaussian process and obeys the Johnson–Nyquistr correlation law (B)C(t)=〈Ĩ(t)Ĩ(0)〉=ℏ2πR∫−∞∞dω ωcothℏω2kBT 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′)limℏ→0C(t)=2kBTRδ(t) the well-known results for white noise are recovered.