Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion

TL;DR

This paper investigates the evolution of density pulses in 1D electron systems after a local quench, revealing wave overturning, oscillations, and the influence of interactions, using simulations, semiclassical, and hydrodynamic models.

Contribution

It demonstrates how density oscillations arise from spectral curvature and population inversion, and how hydrodynamic theory with dispersion captures these effects, including interaction influences.

Findings

Density oscillations have periods much larger than the Fermi wavelength.

Hydrodynamic theory with dispersive terms accurately reproduces oscillation periods.

Strong electron-electron interactions significantly affect the density evolution and oscillation behavior.

Abstract

We explore dynamics of a density pulse induced by a local quench in a one-dimensional electron system. The spectral curvature leads to an "overturn" (population inversion) of the wave. We show that beyond this time the density profile develops strong oscillations with a period much larger than the Fermi wave length. The effect is studied first for the case of free fermions by means of direct quantum simulations and via semiclassical analysis of the evolution of Wigner function. We demonstrate then that the period of oscillations is correctly reproduced by a hydrodynamic theory with an appropriate dispersive term. Finally, we explore the effect of different types of electron-electron interaction on the phenomenon. We show that sufficiently strong interaction [$U(r)\gg 1/mr^2$ where $m$ is the fermionic mass and $r$ the relevant spatial scale] determines the dominant dispersive term in the hydrodynamic equations. Hydrodynamic theory reveals crucial dependence of the density evolution on the relative sign of the interaction and the density perturbation.