  We consider a hydrodynamic model of a quantum dusty plasma. We prove
mathematically that the resulting dust ion acoustic plasma waves present the
property of being conservative on average. Furthermore, we test this property
numerically, confirming its validity. Using standard techniques from the study
of dynamical systems, as for example the Lyapunov characteristic exponents, we
investigate the chaotic dynamics of the plasma and show numerically its
existence for a wide range of parameter values. Finally, we illustrate how
chaotic dynamics organizes in the parameter space for fixed values of the
initial conditions, as the Mach number and the quantum diffraction parameter
are continuously varied.
