Studies On Superconducting Quantum Interference Device System In The Presence Of Thermal Fluctuations

Nonlinear stochastic dynamics theory is one of the important forward subjects in the modern statistical physics. In recent years, some important discovers that acquired through the studied of nonlinear stochastic dynamics, such as noise inducing phase transition, stochastic resonance, nonequilibrium fluctuation induced transport, open up a wide range of applicability of the stochastic theory. The fluctuations (noise) effects becoming quite important along with the raise of temperature in the nonlinear open system. Superconducting quantum interference device is a not only typical but also multi-noise source nonlinear open system. Along with the application of superconductor in liquid Nitrogen temperature turn reality, the thermal fluctuations embodying more and more significantly effect in the superconducting quantum interference device systems. Although the studying of superconducting quantum interference device that using stochastic dynamics is come within star stage in international, but such as the studies on DC SQUID characteristics, the studies on RF SQUID stochastic resonance have become one of the most important forward subjects in the field of high temperature superconducting at present, so applied the latest results of nonlinear stochastic dynamics at the research of SQUID system is a important new point of growth of nonlinear stochastic theory, doubtless, and this make a huge impulsive effects on the study of both experimental and theoretical in the field of high superconducting too.Thus, we have studied the high-Tc superconducting quantum interference device system by stochastic theory, and obtained some significative result, especially the stationary distribution function of DC SQUID is obtained firstly in the accurate theory, and the expressions of all this system's characteristics functions are obtained. The relationship between the optimum bias current and the thermalfluctuation parameter and the range of the optimal reduced inductance arediscovered. In this thesis, the stochastic theory, the SQUID theory and the studies on the high-Tc superconducting quantum interference device that using stochastic theory are systematically reported, which include several aspects:As background of the study, firstly we introduce the stochastic theory of the general nonlinear system; discuss the one dimension nonlinear system and multidimensional nonlinear system's noise, Langevin equations and Fokker-Planck equations, and the steady solution of FPE that satisfied the "potential condition" in multidimensional nonlinear system are obtained. And then discussed the Josephson effect and the superconducting quantum interference effect in chapter 2. In chapter 3 we summarize the model and theory of the supercoducting quantum interference device with two Josephson junctions system (DC SQUID) overall. As the main part of this thesis, based on RSJ model, a symmetric DC SQUID is theoretically studied through two-dimensional Fokker-Planck equations, by using the "potential condition" in the case of steady state, the stationary probability distribution function of this system is obtained firstly in the accurate theory, meanwhile, the expressions of all the SQUID characteristics functions are obtained, for example, the circulating current, total normalized voltage and transfer function. It is found that therelationship between the optimum bias current Iopt and the thermal fluctuation parameter is Iopt / > 1. The optimal reduced DC SQUID inductance opt is in the range of 0.80 < opt < 1.25, which is remarkably agreement with the result of numerical simulation opt 1.