Effect of thermal noise on current-voltage characteristics of Josephson junctions

Measurements are reported of the current-voltage ($I\ensuremath{-}V$) characteristics of externally shunted oxide-barrier tunnel junctions at temperatures $T$ and critical currents ${I}_{c}$ such that the Josephson coupling energy $(\frac{\ensuremath{\hbar}}{2e}){I}_{c}$ is comparable to the thermal energy $kT$. The measurements are in complete quantitative agreement with the theory of Ambegaokar and Halperin in the limit that the dimensionless parameter ${\ensuremath{\beta}}_{c}=(\frac{2e}{\ensuremath{\hbar}})(\frac{{I}_{c}C}{{\ensuremath{\sigma}}^{2}})\ensuremath{\ll}1$, where $C$ is the capacitance and $\ensuremath{\sigma}$ the total conductance of the shunted junction. Measurements for larger values of ${\ensuremath{\beta}}_{c}$ are in qualitative agreement with the theory of Kurkij\"arvi and Ambegaokar. In addition, the Ambegaokar-Halperin theory is generalized to include the $cos\ensuremath{\phi}$ pair-quasiparticle interference term. It is concluded that a measurement of the $cos\ensuremath{\phi}$ term using only the $I\ensuremath{-}V$ characteristic will be difficult.