  The structure of a weak shock in a quantum plasma is studied, taking into
account both dissipation terms due to thermal conduction and dispersive quantum
terms due to the Bohm potential. Unlike quantum systems without dissipations,
even a small thermal conduction may lead to a stationary shock structure. In
the limit of zero quantum effects, the monotonic Burgers solution for the weak
shock is recovered. Still, even small quantum terms make the structure
non-monotonic with the shock driving a train of oscillations into the initial
plasma. The oscillations propagate together with the shock. The oscillations
become stronger as the role of Bohm potential increases in comparison with
thermal conduction. The results could be of importance for laser-plasma
interactions, such as inertial confinement fusion plasmas, and in astrophysical
environments, as well as in condensed matter systems.
