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A nondissipative supercurrent state of a Josephson junction is metastablewith respect to the formation of a finite-resistance state. This transition isdriven by fluctuations, thermal at high temperatures and quantum at lowtemperatures. We evaluate the life time of such a state due to quantumfluctuations in the limit when the supercurrent is approaching the criticalcurrent. The decay probability is determined by the instanton action for thesuperconducting phase difference across the junction. At low temperatures,dynamics of the phase is massive and is determined by the effectivecapacitance, which is a sum of the geometric and intrinsic capacitance of thejunction. We model the central part of the Josephson junction either by anarbitrary short mesoscopic conductor described by the set of its transmissioncoefficients, or by a diffusive wire of an arbitrary length. The intrinsiccapacitance can generally be estimated as $C_* \sim G/E_g$, where $G$ is thenormal-state conductance of the junction and $E_g$ is the proximity minigap inits normal part. The obtained capacitance is sufficiently large toqualitatively explain hysteretic behavior of the current-voltage characteristiceven in the absence of overheating.

Quantum decay of the supercurrent and intrinsic capacitance of Josephson junctions beyond the tunnel limit