The Wigner molecule in a 2D quantum dot

Akman, N
Tomak, Mehmet
The charge density and pair correlation function of three interacting electrons confined within a two-dimensional disc-like hard-wall quantum dot are calculated by full numerical diagonalization of the Hamiltonian. The formation of a Wigner molecule in the form of equilateral triangular configuration for electrons is observed as the size of the dot is increased.


Interacting electrons in a 2D quantum dot
Akman, N; Tomak, Mehmet (1999-04-01)
The exact numerical diagonalization of the Hamiltonian of a 2D circular quantum dot is performed for 2, 3, and 4 electrons. The results an compared with those of the perturbation theory. Our numerical results agree reasonably well for small values of the dimensionless coupling constant lambda = a/a(B) where a is the dot radius and a(B) is the effective Bohr radius. Exact diagonalization results are compared with the classical predictions, and they are found to be almost coincident for large lambda values.
The scaled Hermite–Weber basis in the spectral and pseudospectral pictures
Taşeli, Hasan (Springer Science and Business Media LLC, 2005-10)
Computational efficiencies of the discrete (pseudospectral, collocation) and continuous (spectral, Rayleigh-Ritz, Galerkin) variable representations of the scaled Hermite-Weber basis in finding the energy eigenvalues of Schrodinger operators with several potential functions have been compared. It is well known that the so-called differentiation matrices are neither skew-symmetric nor symmetric in a pseudospectral formulation of a differential equation, unlike their Rayleigh-Ritz counterparts. In spite of th...
The Sigma(0)Lambda transition magnetic moment in light cone QCD sum rules
Alıyev, Tahmasıb; Özpineci, Altuğ; Savcı, Mustafa (2001-09-20)
Using the general form of the Sigma (0) and Lambda currents, the Sigma (0)Lambda transition magnetic moment is calculated in framework of the light cone QCD sum rules. A comparison of our result on this quantity with the existing theoretical results and experimental data is presented.
The discrete fractional Fourier transform
Candan, Çağatay; OZAKTAS, HM (2000-05-01)
We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform generalizes the continuous ordinary Fourier transform. This definition is based on a particular set of eigenvectors of the DFT matrix, which constitutes the discrete counterpart of the set of Hermite-Gaussian functions. The definition is exactly unitary, index additive, and reduces to the DFT for unit ord...
The self-consistent calculation of exchange enhanced odd integer quantized Hall plateaus within Thomas-Fermi-Dirac approximation
Bilgec, G.; Toffoli, Hande; Siddiki, A.; SÖKMEN, İsmail (2010-02-01)
We study the emergent role of many-body effects on a two-dimensional electron gas (2DEG) within the Thomas-Fermi-Dirac-Poisson approximation, including both the exchange and correlation interactions in the presence of a strong perpendicular magnetic field. It is shown that the indirect interactions widen the odd-integer incompressible strips spatially, whereas the even-integer filling factors almost remain unaffected.
Citation Formats
N. Akman and M. Tomak, “The Wigner molecule in a 2D quantum dot,” PHYSICA E, pp. 277–285, 1999, Accessed: 00, 2020. [Online]. Available: