  The dc current-voltage characteristics of small Josephson junctions reveal
features that are not observed in larger junctions, in particular, a switch to
the finite voltage state at current values much less than the expected critical
current of the junction and a finite resistance in the nominally
superconducting regime. Both phenomena are due to the increased sensitivity to
noise associated with the small capacitance of the Josephson junction and have
been extensively studied a few decades ago. Here I focus on the current bias
dependence of the differential resistance of the junction at low current bias
in the nominally superconducting regime, using a quantum Langevin equation
approach that enables a physically transparent incorporation of the noise
environment of the junction. A similar approach might be useful in modeling the
sensitivity of superconducting qubits to noise in the microwave regime.
