  The RCSJ model of resistively and capacitively shunted Josephson junctions is
used to describe superconducting point contacts over a wide range of
resistances up to the metallic -- tunneling transition. Their small dynamic
capacitance of order $C = 0.1 $fF due to the point-contact geometry results in
a huge plasma frequency. The critical current is then strongly suppressed and
the contact resistance becomes finite because of quantum-mechanical zero-point
fluctuations of the Josephson plasma and the rather large escape rate out of
the zero-voltage state due to quantum tunneling. We test the predictions of the
RCSJ model on the classical superconductors lead, indium, aluminum, and
cadmium.
