2,751 research outputs found
Applications of Ideas from Random Matrix Theory to Step Distributions on "Misoriented" Surfaces
Arising as a fluctuation phenomenon, the equilibrium distribution of
meandering steps with mean separation on a "tilted" surface can be
fruitfully analyzed using results from RMT. The set of step configurations in
2D can be mapped onto the world lines of spinless fermions in 1+1D using the
Calogero-Sutherland model. The strength of the ("instantaneous",
inverse-square) elastic repulsion between steps, in dimensionless form, is
. The distribution of spacings between neighboring
steps (analogous to the normalized spacings of energy levels) is well described
by a {\it "generalized" Wigner surmise}: . The value of is taken to best fit the data;
typically . The procedure is superior to conventional
Gaussian and mean-field approaches, and progress is being made on formal
justification. Furthermore, the theoretically simpler step-step distribution
function can be measured and analyzed based on exact results. Formal results
and applications to experiments on metals and semiconductors are summarized,
along with open questions. (conference abstract)Comment: 7 pages, 2 figures; based on talk presented at TH-2002, UNESCO,
Paris, July 2002; to be published in Ann. Henri Poincare
Analytic Formulas for the Orientation Dependence of Step Stiffness and Line Tension: Key Ingredients for Numerical Modeling
We present explicit analytic, twice-differentiable expressions for the
temperature-dependent anisotropic step line tension and step stiffness for the
two principal surfaces of face-centered-cubic crystals, the square {001} and
the hexagonal {111}. These expressions improve on simple expressions that are
valid only for low temperatures and away from singular orientations. They are
well suited for implementation into numerical methods such as finite-element
simulation of step evolution.Comment: 10 pages; reformatted with revtex (with typos corrected) from version
accepted by SIAM--Multiscale Modeling and Simulation on Nov. 21, 2006;
greatly expanded introduction, several minor fixes (mostly stylistic
The evolution of radiation towards thermal equilibrium: A soluble model which illustrates the foundations of Statistical Mechanics
In 1916 Einstein introduced the first rules for a quantum theory of
electromagnetic radiation, and he applied them to a model of matter in thermal
equilibrium with radiation to derive Planck's black-body formula. Einstein's
treatment is extended here to time-dependent stochastic variables, which leads
to a master equation for the probability distribution that describes the
irreversible approach of Einstein's model towards thermal equilibrium, and
elucidates aspects of the foundation of statistical mechanics. An analytic
solution of this equation is obtained in the Fokker-Planck approximation which
is in excellent agreement with numerical results. At equilibrium, it is shown
that the probability distribution is proportional to the total number of
microstates for a given configuration, in accordance with Boltzmann's
fundamental postulate of equal a priori probabilities for these states. While
the counting of these configurations depends on particle statistics- Boltzmann,
Bose-Einstein, or Fermi-Dirac - the corresponding probability is determined
here by the dynamics which are embodied in the form of Einstein's quantum
transition probabilities for the emission and absorption of radiation. In a
special limit, it is shown that the photons in Einstein's model can act as a
thermal bath for the evolution of the atoms towards the canonical equilibrium
distribution of Gibbs. In this limit, the present model is mathematically
equivalent to an extended version of the Ehrenfests' ``dog-flea'' model, which
has been discussed recently by Ambegaokar and Clerk
The Effects of Next-Nearest-Neighbor Interactions on the Orientation Dependence of Step Stiffness: Reconciling Theory with Experiment for Cu(001)
Within the solid-on-solid (SOS) approximation, we carry out a calculation of
the orientational dependence of the step stiffness on a square lattice with
nearest and next-nearest neighbor interactions. At low temperature our result
reduces to a simple, transparent expression. The effect of the strongest trio
(three-site, non pairwise) interaction can easily be incorporated by modifying
the interpretation of the two pairwise energies. The work is motivated by a
calculation based on nearest neighbors that underestimates the stiffness by a
factor of 4 in directions away from close-packed directions, and a subsequent
estimate of the stiffness in the two high-symmetry directions alone that
suggested that inclusion of next-nearest-neighbor attractions could fully
explain the discrepancy. As in these earlier papers, the discussion focuses on
Cu(001).Comment: 8 pages, 3 figures, submitted to Phys. Rev.
Rings sliding on a honeycomb network: Adsorption contours, interactions, and assembly of benzene on Cu(111)
Using a van der Waals density functional (vdW-DF) [Phys. Rev. Lett. 92,
246401 (2004)], we perform ab initio calculations for the adsorption energy of
benzene (Bz) on Cu(111) as a function of lateral position and height. We find
that the vdW-DF inclusion of nonlocal correlations (responsible for dispersive
interactions) changes the relative stability of eight binding-position options
and increases the binding energy by over an order of magnitude, achieving good
agreement with experiment. The admolecules can move almost freely along a
honeycomb web of "corridors" passing between fcc and hcp hollow sites via
bridge sites. Our diffusion barriers (for dilute and two condensed adsorbate
phases) are consistent with experimental observations. Further vdW-DF
calculations suggest that the more compact (hexagonal) Bz-overlayer phase, with
lattice constant a = 6.74 \AA, is due to direct Bz-Bz vdW attraction, which
extends to ~8 \AA. We attribute the second, sparser hexagonal Bz phase, with a
= 10.24 \AA, to indirect electronic interactions mediated by the metallic
surface state on Cu(111). To support this claim, we use a formal
Harris-functional approach to evaluate nonperturbationally the asymptotic form
of this indirect interaction. Thus, we can account well for benzene
self-organization on Cu(111).Comment: 13 pages, 7 figures, 3 tables, submitted for publication Accepted for
publication in Phys. Rev. B. This version contains improved notation (with
corresponding relabeling of figures), very small corrections to some
tabulated values, and corrections concerning lattice lengths and subsequent
discussion of commensurability of unit-cell dimension
Spin-3 Chromium Bose-Einstein Condensates
We analyze the physics of spin-3 Bose-Einstein condensates, and in particular
the new physics expected in on-going experiments with condensates of Chromium
atoms. We first discuss the ground-state properties, which, depending on still
unknown Chromium parameters, and for low magnetic fields can present various
types of phases. We also discuss the spinor-dynamics in Chromium spinor
condensates, which present significant qualitative differences when compared to
other spinor condensates. In particular, dipole-induced spin relaxation may
lead for low magnetic fields to transfer of spin into angular momentum similar
to the well-known Einstein-de Haas effect. Additionally, a rapid large
transference of population between distant magnetic states becomes also
possible.Comment: 4 pages, 3 eps figures. Error in the previous version correcte
Low-Temperature Orientation Dependence of Step Stiffness on {111} Surfaces
For hexagonal nets, descriptive of {111} fcc surfaces, we derive from
combinatoric arguments a simple, low-temperature formula for the orientation
dependence of the surface step line tension and stiffness, as well as the
leading correction, based on the Ising model with nearest-neighbor (NN)
interactions. Our formula agrees well with experimental data for both Ag and
Cu{111} surfaces, indicating that NN-interactions alone can account for the
data in these cases (in contrast to results for Cu{001}). Experimentally
significant corollaries of the low-temperature derivation show that the step
line tension cannot be extracted from the stiffness and that with plausible
assumptions the low-temperature stiffness should have 6-fold symmetry, in
contrast to the 3-fold symmetry of the crystal shape. We examine Zia's exact
implicit solution in detail, using numerical methods for general orientations
and deriving many analytic results including explicit solutions in the two
high-symmetry directions. From these exact results we rederive our simple
result and explore subtle behavior near close-packed directions. To account for
the 3-fold symmetry in a lattice gas model, we invoke a novel
orientation-dependent trio interaction and examine its consequences.Comment: 11 pages, 8 figure
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