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The two-dimensional Wigner crystals are studied with the variational quantum Monte Carlo method. The close relationship between the ground-state wavefunction and the collective excitations in the system is illustrated, and used to guide the construction of the ground-state wavefunction of the strongly correlated solid. Exchange, correlation, and magnetic field effects all give rise to distinct physical phenomena. In the absence of any external magnetic field, interesting spin-orderings are observed in the ground-state of the electron crystal in various two-dimensional lattices. In particular, two-dimensional bipartite lattices are shown not to lead necessarily to an antiferromagnetic ground-state. In the quantum Hall effect regime, a strong magnetic field introduces new energy and length scales. The magnetic field quenches the kinetic energy and poses constraints on how the electrons may correlate with each other. Care is taken to ensure the appropriate translational properties of the wavefunction when the system is in a uniform magnetic field. We have examined the exchange, intra-Landau-level correlation as well as Landau-level-mixing effects with various variational wavefunctions. We also determine their dependences on the experimental parameters such as the carrier effective mass at a modulation-doped semiconductor heterojunction. Our results, when combined with some recent calculations for the energy of the fractional quantum Hall liquid including Landau-level-mixing, show quantitatively that in going from $n$-doping to $p$-doping in $GaAS/AlGaAS$ heterojunction systems, the crossover filling factor from the fractional quantum Hall liquid to the Wigner crystal changes from filling factor $\nu \sim 1/5$ to $\nu \sim 1/3$. This lends strong support to the claim that the, Comment: LaTex file, 14 figures available from zhu@physics.rutgers.edu

We study Escherichia coli chemotaxis behavior in environments with spatially and temporally varying attractant sources by developing a unique microfluidic system. Our measurements reveal a frequency-dependent chemotaxis behavior. At low frequency, the E. coli population oscillates in synchrony with the attractant. In contrast, in fast-changing environments, the population response becomes smaller and out of phase with the attractant waveform. These observations are inconsistent with the well-known Keller-Segel chemotaxis equation. A new continuum model is proposed to describe the population level behavior of E. coli chemotaxis based on the underlying pathway dynamics. With the inclusion of a finite adaptation time and an attractant consumption rate, our model successfully explains the microfluidic experiments at different stimulus frequencies.

The spin orderings of electrons interacting with the long-range 1/[ital r] Coulomb potential on various two-dimensional (2D) lattices are studied with a variational quantum Monte Carlo method. Within the trial wave functions considered, the ground state for a square electron lattice is ferromagnetic, while it is antiferromagnetic for a honeycomb lattice. On a rectangular lattice, the ground state changes from a ferromagnet to an antiferromagnet as the lattice varies from a square to a set of weakly interacting chains. These results indicate the importance of multiple-electron ring-exchange effects for the long-range Coulomb interaction on these 2D lattices.

The valence and core level spectra of chemically prepared, ideally H-terminated Si(111) surfaces are characterized by remarkably sharp features. The valence band levels and their dispersion are well described by first-principles calculations using a quasiparticle self-energy approach within the GW approximation. From the ${\mathrm{Si}}_{2\mathit{p}}$ spectra, an upper limit of 35\ifmmode\pm\else\textpm\fi{}10 meV is derived from the core hole lifetime broadening, a value substantially lower than previously measured.

We report a quasiparticle study of the pressure-induced isostructural insulator-metal transition in solids by the mechanism of band-gap closure. Two examples are investigated: solid Xe and molecular solid hydrogen. The band gaps are calculated with a first-principles quasiparticle approach, in which the electron self-energy operator is expanded to first order in the screened Coulomb interaction, viz., the GW approximation. For the case of solid xenon, the crystal structure has been experimentally established to be hexagonal-close-packed (hcp) in the vicinity of the observed metallization pressure of 132(\ifmmode\pm\else\textpm\fi{}5) GPa. Our calculation for solid xenon yields a metallization pressure of 128 GPa, in good agreement with experiment. The theoretical results further quantitatively explain all the salient features observed in the experimental optical spectra at metallization. For molecular solid hydrogen the structure has yet to be determined definitively. Our calculations are carried out for structures in which hydrogen molecules assume an hcp arrangement. The quasiparticle results are compared with those from Hartree-Fock (HF) and local-density approximation (LDA) calculations.

The surface-state energies of the Ge(111)-2\ifmmode\times\else\texttimes\fi{}1 surface are calculated using a quasiparticle self-energy approach. The surface structural parameters are determined through a local-density-functional total-energy minimization resulting in a buckled \ensuremath{\pi}-bonded-chain geometry. The quasiparticle energies are computed using a first-order expansion of the electron self-energy operator in the screened Coulomb interaction with a model static dielectric matrix. Our calculated surface-state band gaps and dispersions of both the occupied and unoccupied surface states agree well with experiments. Further, the photoelectric threshold \ensuremath{\varphi} is found to be 4.73 eV, compared to 4.74--4.80 eV obtained experimentally.

The pressure coefficients of band gaps of silicon are calculated with use of a first-principles quasiparticle approach. For comparison, the same quantities are also computed within the Hohenberg-Kohn-Sham local-density approximation (LDA). In both cases, the calculations were performed for volumes corresponding to pressures between 0 and 150 kbar using ab initio norm-conserving pseudopotentials. The electron self-energy in the quasiparticle calculation is obtained with use of a first-order expansion in the dressed Green's function G and the screened Coulomb interaction W with local fields. The quasiparticle results show a linear dependence of changes in the band gaps on lattice constant, while the dependence on pressure deviates from linearity at high pressure. The LDA band-gap pressure coefficients, obtained using three commonly used exchange-correlation potential forms, are shown to be very close to the quasiparticle values for the whole range of crystal volumes we considered. At some of the volumes considered, the LDA band gaps are negative. Both sets of pressure-coefficient results are in very good agreement with available experimental values for Si.