Size distribution of sputtered particles from Au nanoislands due to MeV self-ion bombardment

Nanoisland gold films, deposited by vacuum evaporation of gold onto Si(100) substrates, were irradiated with 1.5 MeV Au$^{2+}$ ions up to a fluence of $5\times 10^{14}$ ions cm$^{-2}$ and at incidence angles up to $60^{\circ}$ with respect to the surface normal. The sputtered particles were collected on carbon coated grids (catcher grid) during ion irradiation and were analyzed with transmission electron microscopy and Rutherford backscattering spectrometry. The average sputtered particle size and the areal coverage are determined from transmission electron microscopy measurements, whereas the amount of gold on the substrate is found by Rutherford backscattering spectrometry. The size distributions of larger particles (number of atoms/particle, $n$ $\ge$ 1,000) show an inverse power-law with an exponent of $\sim$ -1 in broad agreement with a molecular dynamics simulation of ion impact on cluster targets.Comment: 13 pages, 8 figures, Submitted for publication in JA

Slice Stretching at the Event Horizon when Geodesically Slicing the Schwarzschild Spacetime with Excision

Slice-stretching effects are discussed as they arise at the event horizon when geodesically slicing the extended Schwarzschild black-hole spacetime while using singularity excision. In particular, for Novikov and isotropic spatial coordinates the outward movement of the event horizon (``slice sucking'') and the unbounded growth there of the radial metric component (``slice wrapping'') are analyzed. For the overall slice stretching, very similar late time behavior is found when comparing with maximal slicing. Thus, the intuitive argument that attributes slice stretching to singularity avoidance is incorrect.Comment: 5 pages, 2 figures, published version including minor amendments suggested by the refere

Vortices in Bose-Einstein condensates - finite-size effects and the thermodynamic limit

For a weakly-interacting Bose gas rotating in a harmonic trap we relate the yrast states of small systems (that can be treated exactly) to the thermodynamic limit (derived within the mean-field approximation). For a few dozens of atoms, the yrast line shows distinct quasi-periodic oscillations with increasing angular momentum that originate from the internal structure of the exact many-body states. These finite-size effects disappear in the thermodynamic limit, where the Gross-Pitaevskii approximation provides the exact energy to leading order in the number of particles N. However, the exact yrast states reveal significant structure not captured by the mean-field approximation: Even in the limit of large N, the corresponding mean-field solution accounts for only a fraction of the total weight of the exact quantum state.Comment: Phys Rev A, in pres

Broken Symmetries in the Reconstruction of v=1 Quantum Hall Edges

Spin-polarized reconstruction of the v=1 quantum Hall edge is accompanied by a spatial modulation of the charge density along the edge. We find that this is also the case for finite quantum Hall droplets: current spin density functional calculations show that the so-called Chamon-Wen edge forms a ring of apparently localized electrons around the maximum density droplet (MDD). The boundaries of these different phases qualitatively agree with recent experiments. For very soft confinement, Chern-Simons Ginzburg-Landau theory indicates formation of a non-translational invariant edge with vortices (holes) trapped in the edge region.Comment: Proceedings of the EP2DS, Ottawa (1999) (submitted to Physica E

Phase transitions in optimal unsupervised learning

We determine the optimal performance of learning the orientation of the symmetry axis of a set of P = alpha N points that are uniformly distributed in all the directions but one on the N-dimensional sphere. The components along the symmetry breaking direction, of unitary vector B, are sampled from a mixture of two gaussians of variable separation and width. The typical optimal performance is measured through the overlap Ropt=B.J* where J* is the optimal guess of the symmetry breaking direction. Within this general scenario, the learning curves Ropt(alpha) may present first order transitions if the clusters are narrow enough. Close to these transitions, high performance states can be obtained through the minimization of the corresponding optimal potential, although these solutions are metastable, and therefore not learnable, within the usual bayesian scenario.Comment: 9 pages, 8 figures, submitted to PRE, This new version of the paper contains one new section, Bayesian versus optimal solutions, where we explain in detail the results supporting our claim that bayesian learning may not be optimal. Figures 4 of the first submission was difficult to understand. We replaced it by two new figures (Figs. 4 and 5 in this new version) containing more detail

Rotating Bose-Einstein condensates: Closing the gap between exact and mean-field solutions

When a Bose-Einstein condensed cloud of atoms is given some angular momentum, it forms vortices arranged in structures with a discrete rotational symmetry. For these vortex states, the Hilbert space of the exact solution separates into a "primary" space related to the mean-field Gross-Pitaevskii solution and a "complementary" space including the corrections beyond mean-field. Considering a weakly-interacting Bose-Einstein condensate of harmonically-trapped atoms, we demonstrate how this separation can be used to close the conceptual gap between exact solutions for systems with only a few atoms and the thermodynamic limit for which the mean-field is the correct leading-order approximation. Although we illustrate this approach for the case of weak interactions, it is expected to be more generally valid.Comment: 8 pages, 5 figure

Density functional theory for strongly-correlated bosonic and fermionic ultracold dipolar and ionic gases

We introduce a density functional formalism to study the ground-state properties of strongly-correlated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling limits. Contrary to conventional density functional approaches, our formalism does not require a previous calculation of the interacting homogeneous gas, and it is thus very suitable to treat systems with tunable long-range interactions. Due to its asymptotic exactness in the regime of strong correlation, the formalism works for systems in which standard mean-field theories fail.Comment: 5 pages, 2 figure

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

Diffusion and Current of Brownian Particles in Tilted Piecewise Linear Potentials: Amplification and Coherence

Overdamped motion of Brownian particles in tilted piecewise linear periodic potentials is considered. Explicit algebraic expressions for the diffusion coefficient, current, and coherence level of Brownian transport are derived. Their dependencies on temperature, tilting force, and the shape of the potential are analyzed. The necessary and sufficient conditions for the non-monotonic behavior of the diffusion coefficient as a function of temperature are determined. The diffusion coefficient and coherence level are found to be extremely sensitive to the asymmetry of the potential. It is established that at the values of the external force, for which the enhancement of diffusion is most rapid, the level of coherence has a wide plateau at low temperatures with the value of the Peclet factor 2. An interpretation of the amplification of diffusion in comparison with free thermal diffusion in terms of probability distribution is proposed.Comment: To appear in PR