Thermal activation and macroscopic quantum tunneling in Josephson junctions

In the present work are collected some recent results obtained concerning the thermal fluctuations and macroscopic quantum tunneling in Josphson systems mostly in connection with their effect on their current-voltage I-V characteristics of a tunnel junction. This study considers both underdamped and overdamped situations looking for proper expressions for the lifetime of both ''locked'' and ''running'' states corresponding to zero and finite voltage current-carrying states of the junction. In this way the authors investigate some aspects of the influence of noise on the I-V curves of Josephson junctions. Using the first-time passage technique developed by Stratonovich expressions which extend the classical Kramers results are obtained. In conclusion, considered is the non-stationary case to explain the presence of hysteresis and sharp transitions in the I-V curves in presence of thermal noise. It is easy to understand how the previous considerations on the activation processes also leads to the stationary case. If during the observations the average on times is larger than both tau-right arrow and tau-left arrow the process is stationary and single-value rounded I-V curves are observed