Numerical Test of Disk Trial Wave function for Half-Filled Landau Level

The analyticity of the lowest Landau level wave functions and the relation between filling factor and the total angular momentum severely limits the possible forms of trial wave functions of a disk of electrons subject to a strong perpendicular magnetic field. For N, the number of electrons, up to 12 we have tested these disk trial wave functions for the half filled Landau level using Monte Carlo and exact diagonalization methods. The agreement between the results for the occupation numbers and ground state energies obtained from these two methods is excellent. We have also compared the profile of the occupation number near the edge with that obtained from a field-theoretical method. The results give qualitatively identical edge profiles. Experimental consequences are briefly discussed.Comment: To be published in Phys. Rev. B. 9 pages, 6 figure

Skyrmions in Higher Landau Levels

We calculate the energies of quasiparticles with large numbers of reversed spins (``skyrmions'') for odd integer filling factors 2k+1, k is greater than or equals 1. We find, in contrast with the known result for filling factor equals 1 (k = 0), that these quasiparticles always have higher energy than the fully polarized ones and hence are not the low energy charged excitations, even at small Zeeman energies. It follows that skyrmions are the relevant quasiparticles only at filling factors 1, 1/3 and 1/5.Comment: 10 pages, RevTe

Unified description of floppy and rigid rotating Wigner molecules formed in quantum dots

Restoration of broken circular symmetry is used to explore the characteristics of the ground states and the excitation spectra of rotating Wigner molecules (RWM's) formed in two-dimensional parabolic N-electron quantum dots. In high magnetic fields, the RWM's are floppy rotors with the energies of the magic angular momentum (L) states obeying aL + b/L^{1/2}. Under such fields the ground-state energies (referenced to the kinetic energy in the lowest Landau level) approach the electrostatic energy of N point charges in the classical equilibrium molecular configuration. At zero field and strong interelectron repulsion, the RWM's behave like quasiclassical rigid rotors whose energies vary as L^2. The particular L-dependence in high B is inherent and natural to a floppy rotating WM, and it can be used as a crucial diagnostic tool for resolving the recently posed question whether the composite-fermion or the RWM picture is appropriate for QD's.Comment: 5 pages. Revtex4 with 3 EPS figures and 2 tables . For related papers, see http://www.prism.gatech.edu/~ph274c

Multiple phase tabu search for bipartite boolean quadratic programming with partitioned variables

The Bipartite Boolean Quadratic Programming Problem with Partitioned Variables (BBQP-PV) is an NP-hard problem with many practical applications. In this study, we present an effective multiple phase tabu search algorithm for solving BBQP-PV. The algorithm is characterized by a joint use of three key components: two tabu search phases that employ a simple neighborhood and a very large-scale neighborhood to achieve search intensification, and a hybrid perturbation phase that adaptively chooses a greedy perturbation or a recency-based perturbation for search diversification. Experimental assessment on 50 standard benchmarks indicates that the proposed algorithm is able to obtain improved lower bounds for 5 instances and match the previously best solutions for most instances, while achieving this performance within competitive time. Additional analysis confirms the importance of the innovative search components

Edge reconstructions in fractional quantum Hall systems

Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations are present. We present a {\it microscopic} calculation of the edge states in the fractional quantum Hall systems at various filling factors using the extended Hamiltonian theory of the fractional quantum Hall effect. We find that at $\nu=1/3$ the quantum Hall edge undergoes a reconstruction as the background potential softens, whereas quantum Hall edges at higher filling factors, such as $\nu=2/5, 3/7$, are robust against reconstruction. We present the results for the dependence of the edge states on various system parameters such as temperature, functional form and range of electron-electron interactions, and the confining potential. Our results have implications for the tunneling experiments into the edge of a fractional quantum Hall system.Comment: 11 pages, 9 figures; minor typos corrected; added 2 reference

Anisotropic Transport of Quantum Hall Meron-Pair Excitations

Double-layer quantum Hall systems at total filling factor $\nu_T=1$ can exhibit a commensurate-incommensurate phase transition driven by a magnetic field $B_{\parallel}$ oriented parallel to the layers. Within the commensurate phase, the lowest charge excitations are believed to be linearly-confined Meron pairs, which are energetically favored to align with $B_{\parallel}$. In order to investigate this interesting object, we propose a gated double-layer Hall bar experiment in which $B_{\parallel}$ can be rotated with respect to the direction of a constriction. We demonstrate the strong angle-dependent transport due to the anisotropic nature of linearly-confined Meron pairs and discuss how it would be manifested in experiment.Comment: 4 pages, RevTex, 3 postscript figure

Composite Fermion Description of Correlated Electrons in Quantum Dots: Low Zeeman Energy Limit

We study the applicability of composite fermion theory to electrons in two-dimensional parabolically-confined quantum dots in a strong perpendicular magnetic field in the limit of low Zeeman energy. The non-interacting composite fermion spectrum correctly specifies the primary features of this system. Additional features are relatively small, indicating that the residual interaction between the composite fermions is weak. \footnote{Published in Phys. Rev. B {\bf 52}, 2798 (1995).}Comment: 15 pages, 7 postscript figure