2,445 research outputs found
Effective way to sum over long range Coulomb potentials in two and three dimensions
I propose a method to calculate logarithmic interaction in two dimensions and
coulomb interaction in three dimensions under periodic boundary conditions.
This paper considers the case of a rectangular cell in two dimensions and an
orthorhombic cell in three dimensions. Unlike the Ewald method, there is no
parameter to be optimized, nor does it involve error functions, thus leading to
the accuracy obtained. This method is similar in approach to that of Sperb [R.
Sperb, Mol. Simulation, 22, 199 (1999).], but the derivation is considerably
simpler and physically appealing. An important aspect of the proposed method is
the faster convergence of the Green function for a particular case as compared
to Sperb's work. The convergence of the sums for the most part of unit cell is
exponential, and hence requires the calculation of only a few dozen terms. In a
very simple way, we also obtain expressions for interaction for systems with
slab geometries. Expressions for the Madelung constant of CsCl and NaCl are
also obtained.Comment: To appear in Phy. Rev.
Wavefront sensing of atmospheric phase distortions at the Palomar 200-in. telescope and implications for adaptive optics
Major efforts in astronomical instrumentation are now being made to apply the techniques of adaptive optics to the correction of phase distortions induced by the turbulent atmosphere and by quasi-static aberrations in telescopes themselves. Despite decades of study, the problem of atmospheric turbulence is still only partially understood. We have obtained video-rate (30 Hz) imaging of stellar clusters and of single-star phase distortions over the pupil of the 200" Hale telescope on Palomar Mountain. These data show complex temporal and spatial behavior, with multiple components arising at a number of scale heights in the atmosphere; we hope to quantify this behavior to ensure the feasibility of adaptive optics at the Observatory. We have implemented different wavefront sensing techniques to measure aperture phase in wavefronts from single stars, including the classical Foucault test, which measures the local gradient of phase, and the recently-devised curvature sensing technique, which measures the second derivative of pupil phase and has formed the real-time wavefront sensor for some very productive astronomical adaptive optics. Our data, though not fast enough to capture all details of atmospheric phase fluctuations, provide important information regarding the capabilities that must be met by the adaptive optics system now being built for the 200" telescope by a team at the Jet Propulsion Lab. We describe our data acquisition techniques, initial results from efforts to characterize the properties of the turbulent atmosphere at Palomar Mountain, and future plans to extract additional quantitative parameters of use for adaptive optics performance predictions
Absence of Domain Wall Roughening in a Transverse Field Ising Model with Long-Range Interactions
We investigate roughening transitions in the context of transverse-field
Ising models. As a modification of the transverse Ising model with short range
interactions, which has been shown to exhibit domain wall roughening, we have
looked into the possibility of a roughening transition for the case of
long-range interactions, since such a system is physically realized in the
insulator LiHoF4. The combination of strong Ising anisotropy and long-range
forces lead naturally to the formation of domain walls but we find that the
long-range forces destroy the roughening transition.Comment: 7 pages, 5 figures, revtex
Enhancement of Wigner crystallization in quasi low-dimensional solids
The crystallization of electrons in quasi low-dimensional solids is studied
in a model which retains the full three-dimensional nature of the Coulomb
interactions. We show that restricting the electron motion to layers (or
chains) gives rise to a rich sequence of structural transitions upon varying
the particle density. In addition, the concurrence of low-dimensional electron
motion and isotropic Coulomb interactions leads to a sizeable stabilization of
the Wigner crystal, which could be one of the mechanisms at the origin of the
charge ordered phases frequently observed in such compounds
Dynamical Diffraction Theory for Wave Packet Propagation in Deformed Crystals
We develop a theory for the trajectory of an x ray in the presence of a
crystal deformation. A set of equations of motion for an x-ray wave packet
including the dynamical diffraction is derived, taking into account the Berry
phase as a correction to geometrical optics. The trajectory of the wave packet
has a shift of the center position due to a crystal deformation. Remarkably, in
the vicinity of the Bragg condition, the shift is enhanced by a factor (: frequency of an x ray, : gap frequency
induced by the Bragg reflection). Comparison with the conventional dynamical
diffraction theory is also made.Comment: 4 pages, 2 figures. Title change
Computer simulations of two-dimensional melting with dipole-dipole interactions
We perform molecular dynamics and Monte Carlo simulations of two-dimensional
melting with dipole-dipole interactions. Both static and dynamic behaviors are
examined. In the isotropic liquid phase, the bond orientational correlation
length 6 and susceptibility 6 are measured, and the data are fitted to the
theoretical ansatz. An algebraic decay is detected for both spatial and
temporal bond orientational correlation functions in an intermediate
temperature regime, and it provides an explicit evidence for the existence of
the hexatic phase. From the finite-size scaling analysis of the global bond
orientational order parameter, the disclination unbinding temperature Ti is
estimated. In addition, from dynamic Monte Carlo simulations of the positional
order parameter, we extract the critical exponents at the dislocation unbinding
temperature Tm. All the results are in agreement with those from experiments
and support the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory.Comment: 23 pages, 12figure
Two-dimensional array of magnetic particles: The role of an interaction cutoff
Based on theoretical results and simulations, in two-dimensional arrangements
of a dense dipolar particle system, there are two relevant local dipole
arrangements: (1) a ferromagnetic state with dipoles organized in a triangular
lattice, and (2) an anti-ferromagnetic state with dipoles organized in a square
lattice. In order to accelerate simulation algorithms we search for the
possibility of cutting off the interaction potential. Simulations on a dipolar
two-line system lead to the observation that the ferromagnetic state is much
more sensitive to the interaction cutoff than the corresponding
anti-ferromagnetic state. For (measured in particle diameters)
there is no substantial change in the energetical balance of the ferromagnetic
and anti-ferromagnetic state and the ferromagnetic state slightly dominates
over the anti-ferromagnetic state, while the situation is changed rapidly for
lower interaction cutoff values, leading to the disappearance of the
ferromagnetic ground state. We studied the effect of bending ferromagnetic and
anti-ferromagnetic two-line systems and we observed that the cutoff has a major
impact on the energetical balance of the ferromagnetic and anti-ferromagnetic
state for . Based on our results we argue that is a
reasonable choice for dipole-dipole interaction cutoff in two-dimensional
dipolar hard sphere systems, if one is interested in local ordering.Comment: 8 page
Laughlin-Jastrow-correlated Wigner crystal in a strong magnetic field
We propose a new ground state trial wavefunction for a two-dimensional Wigner
crystal in a strong perpendicular magnetic field. The wavefunction includes
Laughlin-Jastrow correlations between electron pairs, and may be interpreted as
a crystal state of composite fermions or composite bosons. Treating the power
of the Laughlin-Jastrow factor as a variational parameter, we use quantum
Monte Carlo simulations to compute the energy of these new states. We find that
our wavefunctions have lower energy than existing crystalline wavefunctions in
the lowest Landau level. Our results are consistent with experimental
observations of the filling factor at which the transition between the
fractional quantum Hall liquid and the Wigner crystal occurs for electron
systems. Exchange contributions to the wavefunctions are estimated
quantitatively and shown to be negligible for sufficiently small filling
factors
Theory of paramagnetic scattering in highly frustrated magnets with long-range dipole-dipole interactions: The case of the Tb2Ti2O7, pyrochlore antiferromagnet
Highly frustrated antiferromagnets composed of magnetic rare-earth moments
are currently attracting much experimental and theoretical interest. Rare-earth
ions generally have small exchange interactions and large magnetic moments.
This makes it necessary to understand in detail the role of long-range magnetic
dipole-dipole interactions in these systems, in particular in the context of
spin-spin correlations that develop in the paramagnetic phase, but are often
unable to condense into a conventional long-range magnetic ordered phase. This
scenario is most dramatically emphasized in the frustrated pyrochlore
antiferromagnet material Tb2Ti207 which does not order down to 50 mK despite an
antiferromagnetic Curie-Weiss temperature Tcw ~ -20 K. In this paper we report
results from mean-field theory calculations of the paramagnetic elastic
neutron-scattering in highly frustrated magnetic systems with long-range
dipole-dipole interactions, focusing on the Tb2Ti207 system. Modeling Tb2Ti207
as an antiferromagnetic Ising pyrochlore, we find that the mean-field
paramagnetic scattering is inconsistent with the experimentally observed
results. Through simple symmetry arguments we demonstrate that the observed
paramagnetic correlations in Tb2Ti207 are precluded from being generated by any
spin Hamiltonian that considers only Ising spins, but are qualitatively
consistent with Heisenberg-like moments. Explicit calculations of the
paramagnetic scattering pattern for both Ising and Heisenberg models,
which include finite single-ion anisotropy, support these claims. We offer
suggestions for reconciling the need to restore spin isotropy with the Ising
like structure suggested by the single-ion properties of Tb3+.Comment: Revtex4, 18 pages, 3 eps figures (2 color figures). Change in title
and emphasis on Tb2Ti2O7 only. Spin-ice material removed, to appear in a
later publicatio
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