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

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.

5 figures; references added, outlook section reduced

References in corpus (5)

• Observation of an Efimov-like resonance in ultracold atom-dimer scattering
• Evidence for Universal Four-Body States Tied to an Efimov Trimer
• Efimov Physics in Cold Atoms
• Accumulation of three-body resonances above two-body thresholds
• Charged three-body system with arbitrary masses near conformal invariance

Cited by in corpus (4)

• Comparing and contrasting nuclei and cold atomic gases
• Electric dipole induced universality for Dirac fermions in graphene
• Electron states in the field of charged impurities in two-dimensional Dirac systems
• Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities