Modulation of dust acoustic waves with a quantum correction

Abstract

The one-dimensional quantum hydrodynamic model is considered in the limit of low phase velocity (compared to the Fermi thermal velocities) as well as the limit of low frequency (compared to the particle-neutral collision frequency) to study the amplitude modulation of dust-acoustic waves in a three-species quantum dusty plasma. Using the standard reductive perturbation technique, a nonlinear Schrödinger equation containing the quantum effects is derived. The quantum mechanical effects containing the quantum diffraction and quantum statistics on the modulational instability are studied both analytically and numerically. It is found that quantum effects are to suppress the instability.