Quantum-Noise Theory for the Resistively Shunted Josephson Junction

It is shown that the low-frequency spectral density of the voltage noise in a current-biased Josephson junction with critical current $I_0$, shunt resistance $R$, and small capacitance is $\frac{e{I_0}^2{R}^3}{\pi V}$ in the limit $\mathrm{eV}\gg k_{\mathrm{B}}T{\left(\frac{I}{I_0}\right)}^2$ and $I>\mathrm{}{I}_0$, where $V$ is the voltage and $I$ is the current. The noise arises from zero-point current fluctuations in the shunt resistor. The rounding of the current-voltage characteristic caused by the quantum fluctuations and the effects of nonzero junction capacitance are calculated.