Fingering of Electron Droplets in Nonuniform Magnetic Fields

TL;DR

This paper predicts and demonstrates that in high, nonuniform magnetic fields, electron droplets form fingered patterns and undergo fission, combining semiclassical analysis with simulations to reveal complex quantum behaviors.

Contribution

It introduces a semiclassical framework for predicting fingered pattern formation and droplet fission in electron droplets under nonuniform magnetic fields, supported by explicit pattern construction and simulations.

Findings

Electron droplets form fingered patterns in nonuniform magnetic fields.

Droplet fission occurs at cusp points predicted by semiclassical analysis.

Monte Carlo simulations confirm the quantum breakup phenomenon.

Abstract

A semiclassical analysis of a two-dimensional electron droplet in a high, nonuniform magnetic field predicts that the droplet will form ``fingered'' patterns upon increasing the number of electrons. We construct explicit examples of these patterns using methods first developed for the flow of two-dimensional viscous fluids. We complement our analytical results with Monte Carlo simulations of the droplet wavefunction, and find that at the point where the semiclassical analysis predicts a cusp on the interface, the droplet fissions--a type of ``quantum breakup'' phenomenon.