Energy dissipation of electron solitons in a quantum well

A linear response theory is provided for the dynamic interaction effects of an electron soliton confined in semiconductor quantum well with a conducting surface or a two-dimensional electron gas. It is shown that the soliton-electron-gas effective potential contains a dissipative component resisting against changes of the soliton charge density. Due to the energy dissipation moving solitons are stopped and the nonstationary excitations of the wave packet relax to the standing ground state.

Figure 1

(Color online) (a) Single-electron (dashed curve) and total (dotted curve) energies (left axis) for the inducton scattering from a high potential barrier in the ideal conductor approximation. The position of the inducton center is plotted with the solid line and is referred to the right axis. (b) Potentials stemming from the real (solid line—left axis) and the imaginary (dashed line—right axis) part of the Fourier transform of the induced potential for the inducton charge density (plotted with the dotted line) moving right with momentum $q=0.1k_F$ (see text). (c) Single-electron (dashed curve) and total (dotted curve) energies (left axis) for the free inducton dissipating its kinetic energy via interaction with the electron gas. The solid line shows the momentum (right axis).

Figure 2

(Color online) Total energy (left axis) and momentum normalized to the Fermi momentum (right axis) for the inducton oscillating inside a Gaussian potential cavity.

Figure 3

(Color online) Total energy and single-electron energies for a standing nonstationary inducton relaxing to the stationary ground state.