Multistream model for quantum plasmas

The dynamics of a quantum plasma can be described self-consistently by the nonlinear Schrodinger-Poisson system. We consider a multistream model representing a statistical mixture of N pure states, each described by a wave function. The one-stream and two-stream cases are investigated. We derive the dispersion relation for the two-stream instability and show that a new, purely quantum, branch appears. Numerical simulations of the complete Schrodinger-Poisson system confirm the linear analysis, and provide further results in the strongly nonlinear regime. The stationary states of the Schrodinger-Poisson system are also investigated. These can be viewed as the quantum mechanical counterpart of the classical Bernstein-Greene-Kruskal modes, and are described by a set of coupled nonlinear differential equations for the electrostatic potential and the stream amplitudes.