Variational Method for the Three-Dimensional Many-Electron Dynamics of Semiconductor Quantum Wells

TL;DR

This paper introduces a variational method to analyze the complex three-dimensional electron dynamics in semiconductor quantum wells, focusing on localized density profiles and breathing modes.

Contribution

It develops a self-consistent fluid and variational approach to simplify and characterize electron dynamics in quantum wells, including radial symmetry cases.

Findings

Derived a set of ordinary differential equations for electron fluid dynamics.

Characterized the breathing mode in radially symmetric quantum wells.

Provided insights into the nonlinear behavior of electron gases in nanostructures.

Abstract

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.