2,118 research outputs found
Time evolution of wave-packets in quasi-1D disordered media
We have investigated numerically the quantum evolution of a wave-packet in a
quenched disordered medium described by a tight-binding Hamiltonian with
long-range hopping (band random matrix approach). We have obtained clean data
for the scaling properties in time and in the bandwidth b of the packet width
and its fluctuations with respect to disorder realizations. We confirm that the
fluctuations of the packet width in the steady-state show an anomalous scaling
and we give a new estimate of the anomalous scaling exponent. This anomalous
behaviour is related to the presence of non-Gaussian tails in the distribution
of the packet width. Finally, we have analysed the steady state probability
profile and we have found finite band corrections of order 1/b with respect to
the theoretical formula derived by Zhirov in the limit of infinite bandwidth.
In a neighbourhood of the origin, however, the corrections are .Comment: 19 pages, 9 Encapsulated Postscript figures; submitted to ``European
Physical Journal B'
Coarsening scenarios in unstable crystal growth
Crystal surfaces may undergo thermodynamical as well kinetic,
out-of-equilibrium instabilities. We consider the case of mound and pyramid
formation, a common phenomenon in crystal growth and a long-standing problem in
the field of pattern formation and coarsening dynamics. We are finally able to
attack the problem analytically and get rigorous results. Three dynamical
scenarios are possible: perpetual coarsening, interrupted coarsening, and no
coarsening. In the perpetual coarsening scenario, mound size increases in time
as L=t^n, where the coasening exponent is n=1/3 when faceting occurs, otherwise
n=1/4.Comment: Changes in the final part. Accepted for publication in Phys. Rev.
Let
Disorder regimes and equivalence of disorder types in artificial spin ice
The field-induced dynamics of artificial spin ice are determined in part by
interactions between magnetic islands, and the switching characteristics of
each island. Disorder in either of these affects the response to applied
fields. Numerical simulations are used to show that disorder effects are
determined primarily by the strength of disorder relative to inter-island
interactions, rather than by the type of disorder. Weak and strong disorder
regimes exist and can be defined in a quantitative way.Comment: The following article has been submitted to J. Appl. Phys. After it
is published, it will be found at http://link.aip.org/link/?ja
Diversity enabling equilibration: disorder and the ground state in artificial spin ice
We report a novel approach to the question of whether and how the ground
state can be achieved in square artificial spin ices where frustration is
incomplete. We identify two types of disorder: quenched disorder in the island
response to fields and disorder in the sequence of driving fields. Numerical
simulations show that quenched disorder can lead to final states with lower
energy, and disorder in the driving fields always lowers the final energy
attained by the system. We use a network picture to understand these two
effects: disorder in island responses creates new dynamical pathways, and
disorder in driving fields allows more pathways to be followed.Comment: 5 pages, 5 figure
Vertex dynamics in finite two dimensional square spin ices
Local magnetic ordering in artificial spin ices is discussed from the point
of view of how geometrical frustration controls dynamics and the approach to
steady state. We discuss the possibility of using a particle picture based on
vertex configurations to interpret time evolution of magnetic configurations.
Analysis of possible vertex processes allows us to anticipate different
behaviors for open and closed edges and the existence of different field
regimes. Numerical simulations confirm these results and also demonstrate the
importance of correlations and long range interactions in understanding
particle population evolution. We also show that a mean field model of vertex
dynamics gives important insights into finite size effects.Comment: 4 pages, 4 figures; v2: minor changes to text and figures. Accepted
to Phys. Rev. Let
Dipolar ground state of planar spins on triangular lattices
An infinite triangular lattice of classical dipolar spins is usually
considered to have a ferromagnetic ground state. We examine the validity of
this statement for finite lattices and in the limit of large lattices. We find
that the ground state of rectangular arrays is strongly dependent on size and
aspect ratio. Three results emerge that are significant for understanding the
ground state properties: i) formation of domain walls is energetically favored
for aspect ratios below a critical valu e; ii) the vortex state is always
energetically favored in the thermodynamic limit of an infinite number of
spins, but nevertheless such a configuration may not be observed even in very
large lattices if the aspect ratio is large; iii) finite range approximations
to actual dipole sums may not provide the correct ground sta te configuration
because the ferromagnetic state is linearly unstable and the domain wall energy
is negative for any finite range cutoff.Comment: Several short parts have been rewritten. Accepted for publication as
a Rapid Communication in Phys. Rev.
Stochastic integration for uncoupled continuous-time random walks
Continuous-time random walks are pure-jump processes with several applications in physics, but also in insurance, finance and economics. Based on heuristic considerations, a definition is given for the stochastic integral driven by continuous-time random walks. The martingale properties of the integral are investigated. Finally, it is shown how the definition can be used to easily compute the stochastic integral by means of Monte Carlo simulations.Continuous-time random walks; models of tick-by-tick financial data; stochastic integration
Negative Temperature States in the Discrete Nonlinear Schroedinger Equation
We explore the statistical behavior of the discrete nonlinear Schroedinger
equation. We find a parameter region where the system evolves towards a state
characterized by a finite density of breathers and a negative temperature. Such
a state is metastable but the convergence to equilibrium occurs on astronomical
time scales and becomes increasingly slower as a result of a coarsening
processes. Stationary negative-temperature states can be experimentally
generated via boundary dissipation or from free expansions of wave packets
initially at positive temperature equilibrium.Comment: 4 pages, 5 figure
Coarsening in surface growth models without slope selection
We study conserved models of crystal growth in one dimension [] which are linearly unstable and develop a mound
structure whose typical size L increases in time (). If the local
slope () increases indefinitely, depends on the exponent
characterizing the large behaviour of the surface current (): for and for
.Comment: 7 pages, 2 EPS figures. To be published in J. Phys. A (Letter to the
Editor
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