We have studied the Josephson dynamics of resistively shunted ballisti
c superconducting quantum point contacts at finite temperatures and ar
bitrary number of conducting modes. Compared to the classical Josephso
n dynamics of tunnel junctions, the dynamics of quantum point contacts
exhibits several new features associated with temporal fluctuations o
f the Josephson potential caused by fluctuations in the occupation of
the current-carrying Andreev levels. [S0163-1829(98)01338-1].