  We present a comprehensive theoretical framework for the Andreev bound state
population dynamics in superconducting weak links. Contrary to previous works,
our approach takes into account the generated nonequilibrium distribution of
the continuum quasiparticle states in a self-consistent way. As application of
our theory, we show that the coupling of the superconducting contact to
environmental phase fluctuations induces a charge imbalance of the continuum
quasiparticle population. This imbalance is due to the breaking of the
left-right symmetry in the rates connecting continuum quasiparticles and the
Andreev bound state system, and causes a quasiparticle current on top of the
Josephson current in a ring geometry. We evaluate the phase dependence of the
quasiparticle current for realistic choices of the model parameters. Our theory
also allows one to analyze the quantum coherent evolution of the system from an
arbitrary initial state.
