2,499 research outputs found
The Magnetic Ordering of the 3d Wigner Crystal
Using Path Integral Monte Carlo, we have calculated exchange frequencies as
electrons undergo ring exchanges of 2, 3 and 4 electrons in a ``clean'' 3d
Wigner crystal (bcc lattice) as a function of density. We find pair exchange
dominates and estimate the critical temperature for the transition to
antiferromagnetic ordering to be roughly Ry at melting. In
contrast to the situation in 2d, the 3d Wigner crystal is different from the
solid bcc 3He in that the pair exchange dominates because of the softer
interparticle potential. We discuss implications for the magnetic phase diagram
of the electron gas
Eulerian spectral closures for isotropic turbulence using a time-ordered fluctuation-dissipation relation
Procedures for time-ordering the covariance function, as given in a previous
paper (K. Kiyani and W.D. McComb Phys. Rev. E 70, 066303 (2004)), are extended
and used to show that the response function associated at second order with the
Kraichnan-Wyld perturbation series can be determined by a local (in wavenumber)
energy balance. These time-ordering procedures also allow the two-time
formulation to be reduced to time-independent form by means of exponential
approximations and it is verified that the response equation does not have an
infra-red divergence at infinite Reynolds number. Lastly, single-time
Markovianised closure equations (stated in the previous paper above) are
derived and shown to be compatible with the Kolmogorov distribution without the
need to introduce an ad hoc constant.Comment: 12 page
Anisotropic dynamics of a vicinal surface under the meandering step instability
We investigate the nonlinear evolution of the Bales-Zangwill instability,
responsible for the meandering of atomic steps on a growing vicinal surface. We
develop an asymptotic method to derive, in the continuous limit, an evolution
equation for the two-dimensional step flow. The dynamics of the crystal surface
is greatly influenced by the anisotropy inherent to its geometry, and is
characterized by the coarsening of undulations along the step direction and by
the elastic relaxation in the mean slope direction. We demonstrate, using
similarity arguments, that the coalescence of meanders and the step flow follow
simple scaling laws, and deduce the exponents of the characteristic length
scales and height amplitude. The relevance of these results to experiments is
discussed.Comment: 10 pages, 7 figures; submitted to Phys. Rev.
Low temperature dynamics of kinks on Ising interfaces
The anisotropic motion of an interface driven by its intrinsic curvature or
by an external field is investigated in the context of the kinetic Ising model
in both two and three dimensions. We derive in two dimensions (2d) a continuum
evolution equation for the density of kinks by a time-dependent and nonlocal
mapping to the asymmetric exclusion process. Whereas kinks execute random walks
biased by the external field and pile up vertically on the physical 2d lattice,
then execute hard-core biased random walks on a transformed 1d lattice. Their
density obeys a nonlinear diffusion equation which can be transformed into the
standard expression for the interface velocity v = M[(gamma + gamma'')kappa +
H]$, where M, gamma + gamma'', and kappa are the interface mobility, stiffness,
and curvature, respectively. In 3d, we obtain the velocity of a curved
interface near the orientation from an analysis of the self-similar
evolution of 2d shrinking terraces. We show that this velocity is consistent
with the one predicted from the 3d tensorial generalization of the law for
anisotropic curvature-driven motion. In this generalization, both the interface
stiffness tensor and the curvature tensor are singular at the
orientation. However, their product, which determines the interface velocity,
is smooth. In addition, we illustrate how this kink-based kinetic description
provides a useful framework for studying more complex situations by modeling
the effect of immobile dilute impurities.Comment: 11 pages, 10 figure
Ferromagnetism in the Infinite-U Hubbard Model
We have studied the stability of the ferromagnetic state in the infinite-U
Hubbard model on a square lattice by approximate diagonalization of finite
lattices using the density matrix renormalization group technique. By studying
lattices with up to 5X20 sites, we have found the ferromagnetic state to be
stable below the hole density of 22 percent. Beyond 22 percent of hole doping,
the total spin of the ground state decreased gradually to zero with increasing
hole density.Comment: 13 pages, RevteX 3.0, seven figures appended in uuencoded form,
correcting problems with uuencoded figure
Effect of Rye-Ryegrass Stocking Rate, Breed Types, and Sex of Calf on Feedlot Performance
Last updated: 6/12/200
Symmetry Breaking in Linearly Coupled Dynamical Lattices
We examine one- and two-dimensional (1D and 2D) models of linearly coupled
lattices of the discrete-nonlinear-Schr{\"{o}}dinger type. Analyzing ground
states of the systems with equal powers in the two components, we find a
symmetry-breaking phenomenon beyond a critical value of the squared -norm.
Asymmetric states, with unequal powers in their components, emerge through a
subcritical pitchfork bifurcation, which, for very weakly coupled lattices,
changes into a supercritical one. We identify the stability of various solution
branches. Dynamical manifestations of the symmetry breaking are studied by
simulating the evolution of the unstable branches. The results present the
first example of spontaneous symmetry breaking in 2D lattice solitons. This
feature has no counterpart in the continuum limit, because of the collapse
instability in the latter case.Comment: 9 pages, 9 figures, submitted to Phys. Rev. E, Apr, 200
A Matrix Element for Chaotic Tunnelling Rates and Scarring Intensities
It is shown that tunnelling splittings in ergodic double wells and resonant
widths in ergodic metastable wells can be approximated as easily-calculated
matrix elements involving the wavefunction in the neighbourhood of a certain
real orbit. This orbit is a continuation of the complex orbit which crosses the
barrier with minimum imaginary action. The matrix element is computed by
integrating across the orbit in a surface of section representation, and uses
only the wavefunction in the allowed region and the stability properties of the
orbit. When the real orbit is periodic, the matrix element is a natural measure
of the degree of scarring of the wavefunction. This scarring measure is
canonically invariant and independent of the choice of surface of section,
within semiclassical error. The result can alternatively be interpretated as
the autocorrelation function of the state with respect to a transfer operator
which quantises a certain complex surface of section mapping. The formula
provides an efficient numerical method to compute tunnelling rates while
avoiding the need for the exceedingly precise diagonalisation endemic to
numerical tunnelling calculations.Comment: Submitted to Annals of Physics. This work has been submitted to
Academic Press for possible publicatio
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