Variational method for the three-dimensional many-electron dynamics of semiconductor quantum wells

The three-dimensional nonlinear dynamics of an electron gas in a semiconductor quantum well is analyzed in terms of a self-consistent fluid formulation and a variational approach. Assuming a time-dependent localized profile for the fluid density and appropriated spatial dependences of the scalar potential and fluid velocity, a set of ordinary differential equations is derived. In the radially symmetric case, the prominent features of the associated breathing mode are characterized.