Geometric scaling in the spectrum of an electron captured by a stationary finite dipole

TL;DR

This paper investigates the energy spectrum of an electron near a stationary finite electric dipole, revealing Efimov-like geometric scaling of bound states above a critical dipole moment, with potential realization in quantum dots.

Contribution

It demonstrates the existence of Efimov-like bound states in a non-rotating finite dipole system, highlighting conditions for their emergence and potential physical realizations.

Findings

Bound states appear above a critical dipole moment p_c.

Energy eigenvalues follow an Efimov-like geometric scaling law.

Realistic rotations tend to destroy these properties.

Abstract

We examine the energy spectrum of a charged particle in the presence of a {\it non-rotating} finite electric dipole. For {\emph{any}} value of the dipole moment $p$ above a certain critical value p_{\mathrm{c}}$ an infinite series of bound states arises of which the energy eigenvalues obey an Efimov-like geometric scaling law with an accumulation point at zero energy. These properties are largely destroyed in a realistic situation when rotations are included. Nevertheless, our analysis of the idealised case is of interest because it may possibly be realised using quantum dots as artificial atoms.