90 research outputs found
Metastable and transient states of chemical ordering in Fe-V nanocrystalline alloys
Chemical ordering of the disordered alloys Fe0.78V0.22, Fe0.53V0.47, Fe0.39V0.61, and Fe0.37V0.63 was performed by annealing at temperatures from 723 to 973 K. The initial state of chemical disorder was produced by high-energy ball milling, and the evolution of order was measured by neutron diffractometry and by 57Fe Mössbauer spectrometry. The hyperfine magnetic field distributions obtained from the Mössbauer spectra provided quantitative measurements of the number of antisite Fe atoms in the partially ordered alloys. The long-range order parameters in steady state after long annealing times were used as states of metastable equilibrium for a generally successful comparison with the metastable Fe-V phase diagram calculated by Sanchez et al. [Phys. Rev. B 54, 8958 (1996)]. For the metastable equilibrium state of order in Fe0.53V0.47 at low temperatures, the order parameters were smaller than expected. This corresponded to an abundance of antisite atoms, which were not removed effectively by annealing at the lower temperatures
In an Ising model with spin-exchange dynamics damage always spreads
We investigate the spreading of damage in Ising models with Kawasaki
spin-exchange dynamics which conserves the magnetization. We first modify a
recent master equation approach to account for dynamic rules involving more
than a single site. We then derive an effective-field theory for damage
spreading in Ising models with Kawasaki spin-exchange dynamics and solve it for
a two-dimensional model on a honeycomb lattice. In contrast to the cases of
Glauber or heat-bath dynamics, we find that the damage always spreads and never
heals. In the long-time limit the average Hamming distance approaches that of
two uncorrelated systems. These results are verified by Monte-Carlo
simulations.Comment: 5 pages REVTeX, 4 EPS figures, final version as publishe
Differences between regular and random order of updates in damage spreading simulations
We investigate the spreading of damage in the three-dimensional Ising model
by means of large-scale Monte-Carlo simulations. Within the Glauber dynamics we
use different rules for the order in which the sites are updated. We find that
the stationary damage values and the spreading temperature are different for
different update order. In particular, random update order leads to larger
damage and a lower spreading temperature than regular order. Consequently,
damage spreading in the Ising model is non-universal not only with respect to
different update algorithms (e.g. Glauber vs. heat-bath dynamics) as already
known, but even with respect to the order of sites.Comment: final version as published, 4 pages REVTeX, 2 eps figures include
Chaotic behavior and damage spreading in the Glauber Ising model - a master equation approach
We investigate the sensitivity of the time evolution of a kinetic Ising model
with Glauber dynamics against the initial conditions. To do so we apply the
"damage spreading" method, i.e., we study the simultaneous evolution of two
identical systems subjected to the same thermal noise. We derive a master
equation for the joint probability distribution of the two systems. We then
solve this master equation within an effective-field approximation which goes
beyond the usual mean-field approximation by retaining the fluctuations though
in a quite simplistic manner. The resulting effective-field theory is applied
to different physical situations. It is used to analyze the fixed points of the
master equation and their stability and to identify regular and chaotic phases
of the Glauber Ising model. We also discuss the relation of our results to
directed percolation.Comment: 9 pages RevTeX, 4 EPS figure
The perimeter of large planar Voronoi cells: a double-stranded random walk
Let be the probability for a planar Poisson-Voronoi cell to have
exactly sides. We construct the asymptotic expansion of up to
terms that vanish as . We show that {\it two independent biased
random walks} executed by the polar angle determine the trajectory of the cell
perimeter. We find the limit distribution of (i) the angle between two
successive vertex vectors, and (ii) the one between two successive perimeter
segments. We obtain the probability law for the perimeter's long wavelength
deviations from circularity. We prove Lewis' law and show that it has
coefficient 1/4.Comment: Slightly extended version; journal reference adde
Damage spreading in random field systems
We investigate how a quenched random field influences the damage spreading
transition in kinetic Ising models. To this end we generalize a recent master
equation approach and derive an effective field theory for damage spreading in
random field systems. This theory is applied to the Glauber Ising model with a
bimodal random field distribution. We find that the random field influences the
spreading transition by two different mechanisms with opposite effects. First,
the random field favors the same particular direction of the spin variable at
each site in both systems which reduces the damage. Second, the random field
suppresses the magnetization which, in turn, tends to increase the damage. The
competition between these two effects leads to a rich behavior.Comment: 4 pages RevTeX, 3 eps figure
High-finesse Fabry-Perot cavities with bidimensional SiN photonic-crystal slabs
Light scattering by a two-dimensional photonic crystal slab (PCS) can result in dramatic interference effects associated with Fano resonances. Such devices offer appealing alternatives to distributed Bragg reflectors or filters for various applications such as optical wavelength and polarization filters, reflectors, semiconductor lasers, photodetectors, bio-sensors, or non-linear optical components. Suspended PCSs also find natural applications in the field of optomechanics, where the mechanical modes of a suspended slab interact via radiation pressure with the optical field of a high finesse cavity. The reflectivity and transmission properties of a defect-free suspended PCS around normal incidence can be used to couple out-of-plane mechanical modes to an optical field by integrating it in a free space cavity. Here, we demonstrate the successful implementation of a PCS reflector on a high-tensile stress SiN nanomembrane. We illustrate the physical process underlying the high reflectivity by measuring the photonic crystal band diagram. Moreover, we introduce a clear theoretical description of the membrane scattering properties in the presence of optical losses. By embedding the PCS inside a high-finesse cavity, we fully characterize its optical properties. The spectrally, angular, and polarization resolved measurements demonstrate the wide tunability of the membrane's reflectivity, from nearly 0 to 99.9470~ 0.0025 \%, and show that material absorption is not the main source of optical loss. Moreover, the cavity storage time demonstrated in this work exceeds the mechanical period of low-order mechanical drum modes. This so-called resolved sideband condition is a prerequisite to achieve quantum control of the mechanical resonator with light
A real quaternion spherical ensemble of random matrices
One can identify a tripartite classification of random matrix ensembles into
geometrical universality classes corresponding to the plane, the sphere and the
anti-sphere. The plane is identified with Ginibre-type (iid) matrices and the
anti-sphere with truncations of unitary matrices. This paper focusses on an
ensemble corresponding to the sphere: matrices of the form \bY= \bA^{-1} \bB,
where \bA and \bB are independent matrices with iid standard
Gaussian real quaternion entries. By applying techniques similar to those used
for the analogous complex and real spherical ensembles, the eigenvalue jpdf and
correlation functions are calculated. This completes the exploration of
spherical matrices using the traditional Dyson indices .
We find that the eigenvalue density (after stereographic projection onto the
sphere) has a depletion of eigenvalues along a ring corresponding to the real
axis, with reflective symmetry about this ring. However, in the limit of large
matrix dimension, this eigenvalue density approaches that of the corresponding
complex ensemble, a density which is uniform on the sphere. This result is in
keeping with the spherical law (analogous to the circular law for iid
matrices), which states that for matrices having the spherical structure \bY=
\bA^{-1} \bB, where \bA and \bB are independent, iid matrices the
(stereographically projected) eigenvalue density tends to uniformity on the
sphere.Comment: 25 pages, 3 figures. Added another citation in version
Integrable structure of Ginibre's ensemble of real random matrices and a Pfaffian integration theorem
In the recent publication [E. Kanzieper and G. Akemann, Phys. Rev. Lett. 95, 230201 (2005)], an exact solution was reported for the probability p_{n,k} to find exactly k real eigenvalues in the spectrum of an nxn real asymmetric matrix drawn at
random from Ginibre's Orthogonal Ensemble (GinOE). In the present paper, we offer a detailed derivation of the above result by concentrating on the proof of the Pfaffian integration theorem, the
key ingredient of our analysis of the statistics of real eigenvalues in the GinOE. We also initiate a study of the correlations of complex eigenvalues and derive a formula for the joint probability density function of all complex eigenvalues of a
GinOE matrix restricted to have exactly k real eigenvalues. In the particular case of k=0, all correlation functions of complex eigenvalues are determined
Are Damage Spreading Transitions Generically in the Universality Class of Directed Percolation?
We present numerical evidence for the fact that the damage spreading
transition in the Domany-Kinzel automaton found by Martins {\it et al.} is in
the same universality class as directed percolation. We conjecture that also
other damage spreading transitions should be in this universality class, unless
they coincide with other transitions (as in the Ising model with Glauber
dynamics) and provided the probability for a locally damaged state to become
healed is not zero.Comment: 10 pages, LATE
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