Exact solutions of two electrons in a quantum dot

Zhu, Jia‐Lin; Yu, Jun; Li, Zhiqiang

doi:10.1088/0953-8984/8/42/005

Cited by 38 publications

(29 citation statements)

References 15 publications

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“…For the circular symmetry, the problem of relative motion becomes separable in polar coordinates. Although a closedform solution for the eigenfunctions was obtained with the aid of power series methods [336], the exact energies were calculated numerically. The separability in the case of ω x : ω y = 2 [337] provided a basis for algebraic solutions for certain values of ω x [338].…”

Section: Two-electron Quantum Dot: a New Paradigm In Mesoscopic Physicsmentioning

confidence: 99%

Effects of symmetry breaking in finite quantum systems

2013

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The review considers the peculiarities of symmetry breaking and symmetry transformations and the related physical effects in finite quantum systems. Some types of symmetry in finite systems can be broken only asymptotically. However, with a sufficiently large number of particles, crossover transitions become sharp, so that symmetry breaking happens similarly to that in macroscopic systems. This concerns, in particular, global gauge symmetry breaking, related to Bose-Einstein condensation and superconductivity, or isotropy breaking, related to the generation of quantum vortices, and the stratification in multicomponent mixtures. A special type of symmetry transformation, characteristic only for finite systems, is the change of shape symmetry. These phenomena are illustrated by the examples of several typical mesoscopic systems, such as trapped atoms, quantum dots, atomic nuclei, and metallic grains. The specific features of the review are: (i) the emphasis on the peculiarities of the symmetry breaking in finite mesoscopic systems; (ii) the analysis of common properties of physically different finite quantum systems; (iii) the manifestations of symmetry breaking in the spectra of collective excitations in finite quantum systems. The analysis of these features allows for the better understanding of the intimate relation between the type of symmetry and other physical properties of quantum systems. This also makes it possible to predict new effects by employing the analogies between finite quantum systems of different physical nature.

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Section: Two-electron Quantum Dot: a New Paradigm In Mesoscopic Physicsmentioning

confidence: 99%

Effects of symmetry breaking in finite quantum systems

2013

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“…For general values of this quantity a numerical treatment is required. As mentioned above, the most straightforward one is an integration of the radial equation 7,15 but, nevertheless, other methods such as diagonalization in a basis 16,17 and the Monte Carlo method 18,19 have also been applied. One of us has used the so-called oscillator representation method, perturbatively treating the residual interaction, to derive analytical expressions for the energy levels.…”

Section: Introductionmentioning

confidence: 99%

Roto-vibrational spectrum and Wigner crystallization in two-electron parabolic quantum dots

2004

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We provide a quantitative determination of the crystallization onset for two electrons in a parabolic two-dimensional confinement. This system is shown to be well described by a roto-vibrational model, Wigner crystallization occurring when the rotational motion gets decoupled from the vibrational one. The Wigner molecule thus formed is characterized by its moment of inertia and by the corresponding sequence of rotational excited states. The role of a vertical magnetic field is also considered. Additional support to the analysis is given by the Hartree-Fock phase diagram for the ground state and by the random-phase approximation for the moment of inertia and vibron excitations.

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“…In order to extract the cusp condition, we extrapolate the wave function at the closer I's using the analytically known behavior for a parabolic confinement. 42 Therefore, this method is reliable for smooth potentials that can be approximated by parabolas at a local scale. We have systematically checked the stability of the results by using finer grids in the calculations.…”

Section: Exact Solution For the Two-electron Quantum Ringmentioning

confidence: 99%

Addition energies and density dipole response of quantum rings under the influence of in-plane electric fields

et al. 2007

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Within density functional theory, we address the effect of an in-plane electric field E on the ground state and the density dipole response of a many-electron quantum ring, which is also submitted to a perpendicular magnetic field B. Addition energies and density dipole spectra are discussed as a function of E. For the two-electron case, an exact numerical calculation is performed, obtaining the spin-phase diagram in the E-B plane and showing that transitions between singlet and triplet spin states can be induced by varying the fields. We also find that, in spite of the deformation that E causes in the electronic density, the spin of the ground state of a given electron number ring is very robust, changing little as the strength of the electric field is reasonably increased.

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Exact solutions of two electrons in a quantum dot

Abstract: Making use of the expansion in a power series, the exact eigensolutions of two electrons in a parabolic quantum dot are obtained. The quantum-size effects on the energy spectra of two electrons are shown for the first time.

Cited by 38 publications

References 15 publications

Effects of symmetry breaking in finite quantum systems

Effects of symmetry breaking in finite quantum systems

Roto-vibrational spectrum and Wigner crystallization in two-electron parabolic quantum dots

Addition energies and density dipole response of quantum rings under the influence of in-plane electric fields

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