2,610 research outputs found
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 ions up to a fluence of
ions cm and at incidence angles up to
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, 1,000) show an inverse power-law with an exponent of
-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
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