Numerical integration of quantum hydrodynamic equations involving self-consistent electric field and isothermal pressure for one-dimensional stationary electron motion

摘要

Quantum hydrodynamic equations jointly with the Maxwell divergent equation for an electric field were applied to investigate the one-dimensional stationary isothermal motion of electron fluid. This model system of equations allows study the spatial oscillations (or structures) of the hydrodynamic variables when the electron isothermal pressure is taken into account. We investigated the different regimes of the motion corresponding the weak spatial oscillations about the equilibrium homogeneous state and intensive oscillations. The intensive oscillations were generated at the determined boundary electric fields and the threshold quantities of coordinates. Impulses of the quantum potential had different heights and very large values. In these cases the chaotic oscillations take place. The typical patterns of spatial oscillations, the Fourier-spectra are represented in this paper.