Analysis of a Toy Model of Electron "Splitting"

TL;DR

This paper investigates a simplified quantum model of electron bubble fission in liquid helium, revealing that quantum entanglement dominates over classical descriptions and challenges previous classical assumptions.

Contribution

It introduces a one-dimensional toy model analyzed via the Born-Oppenheimer approximation, demonstrating the quantum nature of electron bubble states contrary to classical predictions.

Findings

Eigenstates are quantum superpositions, not classical bubble separations.

Classical treatment overlooks quantum entanglement in the system.

Quantum analysis contradicts previous classical fission models.

Abstract

We examine Maris' recent suggestion that the fission of electron-inhabited bubbles in liquid helium may give rise to a new form of electron fractionization. We introduce a one-dimensional toy-model--a simplified analogue of the helium system--which may be analyzed using the Born-Oppenheimer approximation. We find that none of the model's low-lying energy eigenstates have the form suggested by Maris' computations, in which the bubbles were treated completely classically. Instead, the eigenstates are quantum-mechanically entangled superposition states, which the classical treatment overlooks.