Effect of colored noise on an overdamped Josephson junction

• Published in: Computer physics communications Vol. 135; no. 1; pp. 35 - 39
• Main Author: Genchev, Z.D.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.03.2001; Elsevier Science
• Subjects: Colored and white noise; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Exact sciences and technology; Fluctuation phenomena, random processes, noise, and brownian motion; Josephson junction; Mathematical methods in physics; Noise-rounded current-voltage curve; Physics; Probability theory, stochastic processes, and statistics; Proximity effects, weak links, tunneling phenomena, and Josephson effects; Proximity effects, weak links, tunneling phenomena, and josephson effects, adreev effect, sn and sns junctions; Statistical physics, thermodynamics, and nonlinear dynamical systems; Stochastic differential equations; Superconductivity; Thermal fluctuations; Thermal fluctuations; Stochastic differential equations; 74.50; Josephson junction; 05.40; 02.50; Noise-rounded current-voltage curve; Colored and white noise; Differential equations; White noise; Theoretical study; Josephson junctions; Color noise; IV characteristic; Temperature fluctuation; Stochastic equation
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/S0010-4655(00)00211-3

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.