Behaviour of three charged particles on a plane under perpendicular magnetic field

We consider the problem of three identical charged particles on a plane under a perpendicular magnetic field and interacting through Coulomb repulsion. This problem is treated within Taut's framework, in the limit of vanishing center of mass vector $\vec{R} \to \vec{0}$, which corresponds to the strong magnetic field limit, occuring for example in the Fractional Quantum Hall Effect. Using the solutions of the biconfluent Heun equation, we compute the eigenstates and show that there is two sets of solutions. The first one corresponds to a system of three independent anyons which have their angular momenta fixed by the value of the magnetic field and specified by a dimensionless parameter $C \simeq \frac{l_B}{l_0}$, the ratio of $l_B$, the magnetic length, over $l_0$, the Bohr radius. This anyonic character, consistent with quantum mechanics of identical particles in two dimensions, is induced by competing physical forces. The second one corresponds to the case of the Landau problem when $C \to 0$. Finally we compare these states with the quantum Hall states and find that the Laughlin wave functions are special cases of our solutions under certains conditions.Comment: 15 pages, 3 figures, Accepeted in JP

Solution of the Schr\"odinger Equation for Quantum Dot Lattices with Coulomb Interaction between the Dots

The Schr\"odinger equation for quantum dot lattices with non-cubic, non-Bravais lattices built up from elliptical dots is investigated. The Coulomb interaction between the dots is considered in dipole approximation. Then only the center of mass (c.m.) coordinates of different dots couple with each other. This c.m. subsystem can be solved exactly and provides magneto- phonon like collective excitations. The inter-dot interaction is involved only through a single interaction parameter. The relative coordinates of individual dots form decoupled subsystems giving rise to intra-dot excitations. As an example, the latter are calculated exactly for two-electron dots. Emphasis is layed on qualitative effects like: i) Influence of the magnetic field on the lattice instability due to inter-dot interaction, ii) Closing of the gap between the lower and the upper c.m. mode at B=0 for elliptical dots due to dot interaction, and iii) Kinks in the single dot excitation energies (versus magnetic field) due to change of ground state angular momentum. It is shown that for obtaining striking qualitative effects one should go beyond simple cubic lattices with spherical dots. We also prove a more general version of the Kohn Theorem for quantum dot lattices. It is shown that for observing effects of electron- electron interaction between the dots in FIR spectra (breaking Kohn's Theorem) one has to consider dot lattices with at least two dot species with different confinement tensors.Comment: 11 figures included as ps-file

Ground State Spin Oscillations of a Two-Electron Quantum Dot in a Magnetic Field

Crossings between spin-singlet and spin-triplet lowest states are analyzed within the model of a two-electron quantum dot in a perpendicular magnetic field. The explicit expressions in terms of the magnetic field, the magnetic quantum number $m$ of the state and the dimensionless dot size for these crossings are found.Comment: 8 pages, 2 figures (PS files). The paper will appear in Journal of Physics: Condensed Matter, volume 11, issue 11 (cover date 22 March 1999) on pages 83 - 8

Two-Electron Quantum Dot in Magnetic Field: Analytical Results

Two interacting electrons in a harmonic oscillator potential under the influence of a perpendicular homogeneous magnetic field are considered. Analytic expressions are obtained for the energy spectrum of the two- and three-dimensional cases. Exact conditions for phase transitions due to the electron-electron interaction in a quantum dot as a function of the dot size and magnetic field are calculated.Comment: 22 pages (Latex file), 3 Postscript figures, to be published in Phys. Rev.B 55, N 20 (1997

Quantum-dot lithium in zero magnetic field: Electronic properties, thermodynamics, and a liquid-solid transition in the ground state

Energy spectra, electron densities, pair correlation functions and heat capacity of a quantum-dot lithium in zero external magnetic field (a system of three interacting two-dimensional electrons in a parabolic confinement potential) are studied using the exact diagonalization approach. A particular attention is given to a Fermi-liquid -- Wigner-solid transition in the ground state of the dot, induced by the intra-dot Coulomb interaction.Comment: 12 pages, incl. 16 figure

Probing the Shape of Quantum Dots with Magnetic Fields

A tool for the identification of the shape of quantum dots is developed. By preparing a two-electron quantum dot, the response of the low-lying excited states to a homogeneous magnetic field, i.e. their spin and parity oscillations, is studied for a large variety of dot shapes. For any geometric configuration of the confinement we encounter characteristic spin singlet - triplet crossovers. The magnetization is shown to be a complementary tool for probing the shape of the dot.Comment: 11 pages, 4 figure

Coulomb correlation effects in semiconductor quantum dots: The role of dimensionality

We study the energy spectra of small three-dimensional (3D) and two-dimensional (2D) semiconductor quantum dots through different theoretical approaches (single-site Hubbard and Hartree-Fock hamiltonians); in the smallest dots we also compare with exact results. We find that purely 2D models often lead to an inadequate description of the Coulomb interaction existing in realistic structures, as a consequence of the overestimated carrier localization. We show that the dimensionality of the dots has a crucial impact on (i) the accuracy of the predicted addition spectra; (ii) the range of validity of approximate theoretical schemes. When applied to realistic 3D geometries, the latter are found to be much more accurate than in the corresponding 2D cases for a large class of quantum dots; the single-site Hubbard hamiltonian is shown to provide a very effective and accurate scheme to describe quantum dot spectra, leading to good agreement with experiments.Comment: LaTeX 2.09, RevTeX, 25 pages, 9 Encapsulated Postscript figures. To be published in Physical Review

Porphyromonas gingivalis oral infection exacerbates the development and severity of collagen-induced arthritis

Abstract Introduction Clinical studies suggest a direct influence of periodontal disease (PD) on serum inflammatory markers and disease assessment of patients with established rheumatoid arthritis (RA). However, the influence of PD on arthritis development remains unclear. This investigation was undertaken to determine the contribution of chronic PD to immune activation and development of joint inflammation using the collagen-induced arthritis (CIA) model. Methods DBA1/J mice orally infected with Porphyromonas gingivalis were administered with collagen II (CII) emulsified in complete Freund’s adjuvant (CFA) or incomplete Freund’s adjuvant (IFA) to induce arthritis. Arthritis development was assessed by visual scoring of paw swelling, caliper measurement of the paws, mRNA expression, paw micro-computed tomography (micro-CT) analysis, histology, and tartrate resistant acid phosphatase for osteoclast detection (TRAP)-positive immunohistochemistry. Serum and reactivated splenocytes were evaluated for cytokine expression. Results Mice induced for PD and/or arthritis developed periodontal disease, shown by decreased alveolar bone and alteration of mRNA expression in gingival tissues and submandibular lymph nodes compared to vehicle. P. gingivalis oral infection increased paw swelling and osteoclast numbers in mice immunized with CFA/CII. Arthritis incidence and severity were increased by P. gingivalis in mice that received IFA/CII immunizations. Increased synovitis, bone erosions, and osteoclast numbers in the paws were observed following IFA/CII immunizations in mice infected with P gingivalis. Furthermore, cytokine analysis showed a trend toward increased serum Th17/Th1 ratios when P. gingivalis infection was present in mice receiving either CFA/CII or IFA/CII immunizations. Significant cytokine increases induced by P. gingivalis oral infection were mostly associated to Th17-related cytokines of reactivated splenic cells, including IL-1β, IL-6, and IL-22 in the CFA/CII group and IL-1β, tumor necrosis factor-α, transforming growth factor-β, IL-6 and IL-23 in the IFA/CII group. Conclusions Chronic P. gingivalis oral infection prior to arthritis induction increases the immune system activation favoring Th17 cell responses, and ultimately accelerating arthritis development. These results suggest that chronic oral infection may influence RA development mainly through activation of Th17-related pathways.http://deepblue.lib.umich.edu/bitstream/2027.42/112639/1/13075_2013_Article_4062.pd