Harmonic oscillator eigenfunction expansions, quantum dots, and effective interactions

Abstract

We give a thorough analysis of the convergence properties of the configuration-interaction method as applied to parabolic quantum dots among other systems, including \emph{a priori} error estimates. The method converges slowly in general, and in order to overcome this, we propose to use an effective two-body interaction well-known from nuclear physics. Through numerical experiments we demonstrate a significant increase in accuracy of the configuration interaction method.

3 figures

References in corpus (8)

• The Shell Model as Unified View of Nuclear Structure
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• Quantum-dot lithium in zero magnetic field: Electronic properties, thermodynamics, and a liquid-solid transition in the ground state
• Two-electron lateral quantum-dot molecules in a magnetic field
• Two ground-state modifications of quantum-dot beryllium
• Configuration interaction method for Fock-Darwin states
• Geometry of effective Hamiltonians
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Cited by in corpus (14)

• Coupled-cluster computations of atomic nuclei
• Convergence properties of {\itshape ab initio} calculations of light nuclei in a harmonic oscillator basis
• Surface Symmetry Energy of Nuclear Energy Density Functionals
• Emergent properties of nuclei from ab initio coupled-cluster calculations
• Living on the edge of stability, the limits of the nuclear landscape
• Ab initio computation of circular quantum dots
• Properties of infrared extrapolations in a harmonic oscillator basis
• Performance of the coupled cluster singles and doubles method on two-dimensional quantum dots
• Basis-set correction based on density-functional theory: Rigorous framework for a one-dimensional model
• Many-body interactions and nuclear structure
• Coupled cluster theory for the ground and excited states of two dimensional quantum dots
• Addition and removal energies of circular quantum dots
• Improved convergence of scattering calculations in the oscillator representation
• Back-action effects in cavity-coupled quantum conductors