3,240 research outputs found
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
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.
Schrodinger equation for the one particle density matrix of thermal systems: An alternative formulation of Bose-Einstein condensation
We formulate a linear Schrodinger equation with the temperature-dependent
potential for the one-particle density matrix and obtain the condensation
temperature of the Bose-Einstein condensate from a bound-state condition for
the Schrodinger equation both with and without the confining trap. The results
are in very good agreement with those of the full statistical physics
treatment. This is an alternative to the Bose-Einstein condensation in the
standard ideal Bose gas treatment.Comment: 4 pages, 2 figure
Einstein's fluctuation formula. A historical overview
A historical overview is given on the basic results which appeared by the
year 1926 concerning Einstein's fluctuation formula of black-body radiation, in
the context of light-quanta and wave-particle duality. On the basis of the
original publications (from Planck's derivation of the black-body spectrum and
Einstein's introduction of the photons up to the results of Born, Heisenberg
and Jordan on the quantization of a continuum) a comparative study is presented
on the first line of thoughts that led to the concept of quanta. The nature of
the particle-like fluctuations and the wave-like fluctuations are analysed by
using several approaches. With the help of the classical probability theory, it
is shown that the infinite divisibility of the Bose distribution leads to the
new concept of classical poissonian photo-multiplets or to the binary
photo-multiplets of fermionic character. As an application, Einstein's
fluctuation formula is derived as a sum of fermion type fluctuations of the
binary photo-multiplets.Comment: 34 page
Reply to "Can gravitational dynamics be obtained by diffeomorphism invariance of action?"
In a previous work we showed that, in a suitable setting, one can use
diffeomorphism invariance in order to derive gravitational field equations from
boundary terms of the gravitational action. Standing by our results we reply
here to a recent comment questioning their validity.Comment: Accepted for publication in PR
On the interaction of a single-photon wave packet with an excited atom
The interaction of a single-photon wave packet with an initially excited
two-level atom in free space is studied in semiclassical and quantum
approaches. It is shown that the final state of the field does not contain
doubly occupied modes. The process of the atom's transition to the ground state
may be accelerated, decelerated or even reversed by the incoming photon,
depending on parameters. The spectrum of emitted radiation is close to the sum
of the spectrum of the incoming single-photon wave packet and the natural line
shape, with small and complicated deviations.Comment: 17 pages, 5 figure
Irreducible decomposition of Gaussian distributions and the spectrum of black-body radiation
It is shown that the energy of a mode of a classical chaotic field, following
the continuous exponential distribution as a classical random variable, can be
uniquely decomposed into a sum of its fractional part and of its integer part.
The integer part is a discrete random variable (we call it Planck variable)
whose distribution is just the Bose distribution yielding the Planck law of
black-body radiation. The fractional part is the dark part (we call is dark
variable) with a continuous distribution, which is, of course, not observed in
the experiments. It is proved that the Bose distribution is infinitely
divisible, and the irreducible decomposition of it is given. The Planck
variable can be decomposed into an infinite sum of independent binary random
variables representing the binary photons (more accurately photo-molecules or
photo-multiplets) of energies 2^s*h*nu with s=0,1,2... . These binary photons
follow the Fermi statistics. Consequently, the black-body radiation can be
viewed as a mixture of statistically and thermodynamically independent fermion
gases consisting of binary photons. The binary photons give a natural tool for
the dyadic expansion of arbitrary (but not coherent) ordinary photon
excitations. It is shown that the binary photons have wave-particle
fluctuations of fermions. These fluctuations combine to give the wave-particle
fluctuations of the original bosonic photons expressed by the Einstein
fluctuation formula.Comment: 29 page
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
Field equations from a surface term
As is well known, in order for the Einstein--Hilbert action to have a well
defined variation, and therefore to be used for deriving field equation through
the stationary action principle, it has to be amended by the addition of a
suitable boundary term. It has recently been claimed that, if one constructs an
action by adding this term to the matter action, the Einstein field equations
can be derived by requiring this action to be invariant under active
transformations which are normal to a null boundary. In this paper we
re-examine this approach both for the case of pure gravity and in the presence
of matter. We show that in the first case this procedure holds for more general
actions than the Einstein-Hilbert one and trace the basis of this remarkable
attribute. However, it is also pointed out the when matter is rigorously
considered the approach breaks down. The reasons for that are thoroughly
discussed.Comment: Typos corrected, minor changes to match published versio
Response of the Shockley surface state to an external electrical field: A density-functional theory study of Cu(111)
The response of the Cu(111) Shockley surface state to an external electrical
field is characterized by combining a density-functional theory calculation for
a slab geometry with an analysis of the Kohn-Sham wavefunctions. Our analysis
is facilitated by a decoupling of the Kohn-Sham states via a rotation in
Hilbert space. We find that the surface state displays isotropic dispersion,
quadratic until the Fermi wave vector but with a significant quartic
contribution beyond. We calculate the shift in energetic position and effective
mass of the surface state for an electrical field perpendicular to the Cu(111)
surface; the response is linear over a broad range of field strengths. We find
that charge transfer occurs beyond the outermost copper atoms and that
accumulation of electrons is responsible for a quarter of the screening of the
electrical field. This allows us to provide well-converged determinations of
the field-induced changes in the surface state for a moderate number of layers
in the slab geometry.Comment: 11 pages, 6 figures, 4 tables; accepted for publication by Phys. Rev.
B; changes from v1 in response to referee comments, esp. to Sections I and
V.B (inc. Table 4), with many added references, but no change in results or
conclusion
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