64 research outputs found
Ising-like dynamics and frozen states in systems of ultrafine magnetic particles
We use Monte-Carlo simulations to study aging phenomena and the occurence of
spinglass phases in systems of single-domain ferromagnetic nanoparticles under
the combined influence of dipolar interaction and anisotropy energy, for
different combinations of positional and orientational disorder. We find that
the magnetic moments oriente themselves preferably parallel to their anisotropy
axes and changes of the total magnetization are solely achieved by 180 degree
flips of the magnetic moments, as in Ising systems. Since the dipolar
interaction favorizes the formation of antiparallel chain-like structures,
antiparallel chain-like patterns are frozen in at low temperatures, leading to
aging phenomena characteristic for spin-glasses. Contrary to the intuition,
these aging effects are more pronounced in ordered than in disordered
structures.Comment: 5 pages, 6 figures. to appear in Phys. Rev.
Frozen metastable states in ordered systems of ultrafine magnetic particles
For studying the interplay of dipolar interaction and anisotropy energy in
systems of ultrafine magnetic particles we consider simple cubic systems of
magnetic dipoles with anisotropy axes pointing into the -direction. Using
Monte Carlo simulations we study the magnetic relaxation from several initial
states. We show explicitely that, due to the combined influence of anisotropy
energy and dipole interaction, magnetic chains are formed along the
-direction that organize themselves in frozen metastable domains of columnar
antiferromagnetic order. We show that the domains depend explicitely on the
history and relax only at extremely large time scales towards the ordered
state. We consider this as an indication for the appearence of frozen
metastable states also in real sytems, where the dipoles are located in a
liquid-like fashion and the anisotropy axes point into random directions
A renormalization approach for the 2D Anderson model at the band edge: Scaling of the localization volume
We study the localization volumes (participation ratio) of electronic
wave functions in the 2d-Anderson model with diagonal disorder. Using a
renormalization procedure, we show that at the band edges, i.e. for energies
, is inversely proportional to the variance \var of the
site potentials. Using scaling arguments, we show that in the neighborhood of
, scales as V=\var^{-1}g((4-\ve E\ve)/\var) with the scaling
function . Numerical simulations confirm this scaling ansatz
Periodic orbit theory in fractal drum
The level statistics of pseudointegrable fractal drums is studied numerically
using periodic orbit theory. We find that the spectral rigidity ,
which is a measure for the correlations between the eigenvalues, decreases to
quite small values (as compared to systems with only small boundary roughness),
thereby approaching the behavior of chaotic systems. The periodic orbit results
are in good agreement with direct calculations of from the
eigenvalues.Comment: to appear in Physica
Periodic orbit theory and spectral rigidity in pseudointegrable systems
We calculate numerically the periodic orbits of pseudointegrable systems of
low genus numbers that arise from rectangular systems with one or two
salient corners. From the periodic orbits, we calculate the spectral rigidity
using semiclassical quantum mechanics with reaching up to
quite large values. We find that the diagonal approximation is applicable when
averaging over a suitable energy interval. Comparing systems of various shapes
we find that our results agree well with calculated directly from
the eigenvalues by spectral statistics. Therefore, additional terms as e.g.
diffraction terms seem to be small in the case of the systems investigated in
this work. By reducing the size of the corners, the spectral statistics of our
pseudointegrable systems approaches the one of an integrable system, whereas
very large differences between integrable and pseudointegrable systems occur,
when the salient corners are large. Both types of behavior can be well
understood by the properties of the periodic orbits in the system
Application of the Trace Formula in Pseudointegrable Systems
We apply periodic-orbit theory to calculate the integrated density of states
from the periodic orbits of pseudointegrable polygon and barrier
billiards. We show that the results agree so well with the results obtained
from direct diagonalization of the Schr\"odinger equation, that about the first
100 eigenvalues can be obtained directly from the periodic-orbit calculations
in good accuracy.Comment: 5 Pages, 4 Figures, submitted to Phys. Rev.
Scaling of the localization length in linear electronic and vibrational systems with long-range correlated disorder
The localization lengths of long-range correlated disordered chains are
studied for electronic wavefunctions in the Anderson model and for vibrational
states. A scaling theory close to the band edge is developed in the Anderson
model and supported by numerical simulations. This scaling theory is mapped
onto the vibrational case at small frequencies. It is shown that for small
frequencies, unexpectateley the localization length is smaller for correlated
than for uncorrelated chains.Comment: to be published in PRB, 4 pages, 2 Figure
Vibrational Excitations in Percolation: Localization and Multifractality
We discuss localized excitations on the incipient infinite percolation cluster. Assuming a simple exponential decay of the amplitudes ψi in terms of the chemical (minimal) path, we show theoretically that the ψ’s are characterized by a logarithmically broad distribution, and display multifractal features as a function of the Euclidean distance. The moments of ψi exhibit novel crossover phenomena. Our numerical simulations of fractons exhibit a nontrivial distribution of localization lengths, even when the chemical distance is fixed. These results are explained via a generalization of the theory
Correlating self- and transport diffusion in the Knudsen regime
Comparing the rates of molecular diffusion in porous materials under different regimes of measurement may provide valuable information about the underlying mechanisms. After quite generally explaining the benefit of such a procedure, we refer to a case which in the last few years has raised controversial discussion within the community, viz. the comparison of diffusion phenomena in pores of varying roughness in
the so-called Knudsen regime. Knudsen diffusion represents the limiting case of molecular diffusion in pores, where mutual encounters of the molecules within the free pore space may be neglected and the time of flight between subsequent collisions with the pore walls significantly exceeds the interaction time between the pore wall and the molecules. In our studies, the coefficients of self- and transport diffusion are found to be in satisfactory agreement, which contradicts previous literature data. A number of effects which might becloud this relationship are discussed
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