Many-electron ground states in anisotropic parabolic quantum dots

Fujito, Masamichi; Natori, Akiko; Yasunaga, Hitoshi

doi:10.1103/physrevb.53.9952

Cited by 109 publications

(55 citation statements)

References 20 publications

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“…In practice they have been used for up to 8 electrons 7,8 , but the accuracy is very limited for all except N ≤ 3. Hartree 9 , restricted Hartree-Fock (HF), spin-and/or-space unrestricted Hartree-Fock [10][11][12] (UHF) and local spin-density (LSDA) and current density functional methods [13][14][15] , give results that are satisfactory for a qualitative understanding of some systematic properties. However, comparisons with exact results show discrepancies in the energies that are substantial on the scale of energy differences.…”

Section: Introductionmentioning

confidence: 99%

Diffusion Monte Carlo study of circular quantum dots

2000

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We present ground and excited state energies obtained from Diffusion Monte Carlo (DMC) calculations, using accurate multiconfiguration wave functions, for N electrons (N ≤ 13) confined to a circular quantum dot. We compare the density and correlation energies to the predictions of local spin density approximation theory (LSDA), and Hartree-Fock theory (HF), and analyze the electron-electron pair-correlation functions. The DMC estimated change in electrochemical potential as a function of the number of electrons in the dot is compared to that from LSDA and HF calculations. Hund's first rule is found to be satisfied for all dots except N = 4 for which there is a near degeneracy. 85.30.Vw,

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Section: Introductionmentioning

confidence: 99%

Diffusion Monte Carlo study of circular quantum dots

2000

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“…The addition energy ͑N͒ is defined to be the energy needed to add an electron into ͑N −1͒ electron system, namely, ͑N͒ = E tot ͑N͒ − E tot ͑N −1͒, where, E tot ͑N͒ is the total energy of the N-electron quantum dot. Several recent theoretical studies have explored the shell-filling behavior of a few-electron ͑less than 20͒ quantum dots using the conventional LSDA or GGA energy functional, [54][55][56] but no detailed exploration has been performed on the general shell-filling behavior of many-electron quantum dots. In a recent study, we extended the OEP/KLI-SIC formalism to the study of the electronic structure and shell-filling behavior of quantum dots with N = 2-60.…”

Section: Electronic Structure Of Quantum Dotsmentioning

confidence: 99%

Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields

Chu¹

2005

The Journal of Chemical Physics

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A critical re-assignment of the Rydberg states of iodomethane based on new polarization data J. Chem. Phys. 138, 134308 (2013) In this paper, we present a short account of some recent developments of self-interaction-free density-functional theory ͑DFT͒ and time-dependent density-functional theory ͑TDDFT͒ for accurate and efficient treatment of the electronic structure, and time-dependent quantum dynamics of many-electron atomic and molecular systems. The conventional DFT calculations using approximate and explicit exchange-correlation energy functional contain spurious self-interaction energy and improper long-range asymptotic potential, preventing reliable treatment of the excited, resonance, and continuum states. We survey some recent developments of DFT/TDDFT with optimized effective potential ͑OEP͒ and self-interaction correction ͑SIC͒ for both atomic and molecular systems for overcoming some of the above mentioned difficulties. These DFT ͑TDDFT͒/ OEP-SIC approaches allow the use of orbital-independent single-particle local potential which is self-interaction free. In addition we discuss several numerical techniques recently developed for efficient and high-precision treatment of the self-interaction-free DFT/TDDFT equations. The usefulness of these procedures is illustrated by a few case studies of atomic, molecular, and condensed matter processes of current interests, including ͑a͒ autoionizing resonances, ͑b͒ relativistic OEP-SIC treatment of atomic structure ͑Z = 2-106͒, ͑c͒ shell-filling electronic structure in quantum dots, ͑d͒ atomic and molecular processes in intense laser fields, including multiphoton ionization, and very-high-order harmonic generation, etc. For the time-dependent processes, an alternative Floquet formulation of TDDFT is introduced for time-independent treatment of multiphoton processes in intense periodic or quasiperiodic fields. We conclude this paper with some open questions and perspectives of TDDFT.

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“…During last few decades many theoretical and experimental studies on QDs have been performed within parabolic confinement models as well as beyond this approximation. Both the 2D and 3D QD's have been investigated in a framework of strict quantum-mechanical and semiclassical approaches, including also effects of an external magnetic field [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Semiclassical solutions for a two-electron QD in a magnetic field have been investigated in terms of action-angle variables using the classical adiabatic approximation [19].…”

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confidence: 99%

Two-Electron Spherical Quantum Dot in a Magnetic Field

Poszwa

2016

Few-Body Syst

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We investigate three-dimensional, two-electron quantum dots in an external magnetic field B. Due to mixed spherical and cylindrical symmetry the Schrödinger equation is not completely separable. Highly accurate numerical solutions, for a wide range of B, have been obtained by the expansion of wavefunctions in double-power series and by imposing on the radial functions appropriate boundary conditions. The asymptotic limit of a very strong magnetic field and the 2D approach have been considered. Ground state properties of the two-electron semiconductor quantum dots are investigated using both the 3D and 2D models. Theoretical calculations have been compared with recent experimental results. IntroductionThe influence of spatial confinement on properties of quantum systems have been widely studied in the literature and remains subject of continuous interest in both theoretical and experimental fields [1][2][3][4][5]. One of the most interesting confined quantum systems is the two-electron Hooke's-law atom (HA) also known as hookium or harmonium [6]. The HA refers to a model system composed of two electrons interacting by the Coulombic potential and confined in an external harmonic potential. Many applications for this system ensues from some unique properties of the HA. For the parabolic confinement the two-electron Hamiltonian separates. This property significantly simplifies the two-particle Schrödinger equation leading, in fact, to the one-dimensional radial problem. We note that the separability of the Schrödinger equation describing many interacting particles is rather exceptional. In particular, it is possible when interactions between disjoint pairs of particles, interacting by arbitrary two-particle potentials, are harmonic [7,8]. For the HA the Schrödinger equation not only separates exactly but also, for a set of the coupling constants, closed-form analytical solutions exist [9,10]. This is of particular importance for the understanding of the role of electron-electron interaction and correlation effects.When the electron mass is replaced by the relevant effective mass and the e-e interaction coupling constant is supplemented by the dielectric constant of semiconductor, the HA atom may be regarded to as a twoelectron quantum dot (QD). During last few decades many theoretical and experimental studies on QDs have been performed within parabolic confinement models as well as beyond this approximation. Both the 2D and 3D QD's have been investigated in a framework of strict quantum-mechanical and semiclassical approaches, including also effects of an external magnetic field [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Semiclassical solutions for a two-electron QD in a magnetic field have been investigated in terms of action-angle variables using the classical adiabatic approximation [19]. Spin-singlet and spin-triplet transitions have been studied and the magnetic moment and susceptibility have been obtained as functions of the magnetic field [20].A.

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Many-electron ground states in anisotropic parabolic quantum dots

Cited by 109 publications

References 20 publications

Diffusion Monte Carlo study of circular quantum dots

Diffusion Monte Carlo study of circular quantum dots

Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields

Two-Electron Spherical Quantum Dot in a Magnetic Field

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