Semiclassical analysis of a two-electron quantum dot in a magnetic field: dimensional phenomena

Abstract

While the dynamics for three-dimensional axially symmetric two-electron quantum dots with parabolic confinement potentials is in general non-separable we have found an exact separability with three quantum numbers for specific values of the magnetic field. Furthermore, it is shown that the magnetic properties such as the magnetic moment and the susceptibility are sensitive to the presence and strength of a vertical confinement. Using a semiclassical approach the calculation of the eigenvalues reduces to simple quadratures providing a transparent and almost analytical quantization of the quantum dot energy levels which differ from the exact energies only by a few percent.

10 pages, 1 figure (gif), 3 figures (eps)

References in corpus (1)

• The Statistical Theory of Quantum Dots

Cited by in corpus (10)

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• Hidden symmetries of two-electron quantum dots in a magnetic field
• Finite-thickness effects in ground-state transitions of two-electron quantum dots
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• Spectra of Harmonium in a magnetic field using an initial value representation of the semiclassical propagator
• Non-Markovian feature of the classical Hall effect
• Open quantum system in external magnetic field within non-Markovian quantum Langevin approach
• A geometrical crossover in excited states of two-electron quantum dots in a magnetic field
• Chaotic properties of Coulomb-interacting circular billiards