1,544 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'
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.
Energy diffusion in hard-point systems
We investigate the diffusive properties of energy fluctuations in a
one-dimensional diatomic chain of hard-point particles interacting through a
square--well potential. The evolution of initially localized infinitesimal and
finite perturbations is numerically investigated for different density values.
All cases belong to the same universality class which can be also interpreted
as a Levy walk of the energy with scaling exponent 3/5. The zero-pressure limit
is nevertheless exceptional in that normal diffusion is found in tangent space
and yet anomalous diffusion with a different rate for perturbations of finite
amplitude. The different behaviour of the two classes of perturbations is
traced back to the "stable chaos" type of dynamics exhibited by this model.
Finally, the effect of an additional internal degree of freedom is
investigated, finding that it does not modify the overall scenarioComment: 16 pages, 15 figure
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
Nonequilibrium dynamics of a stochastic model of anomalous heat transport: numerical analysis
We study heat transport in a chain of harmonic oscillators with random
elastic collisions between nearest-neighbours. The equations of motion of the
covariance matrix are numerically solved for free and fixed boundary
conditions. In the thermodynamic limit, the shape of the temperature profile
and the value of the stationary heat flux depend on the choice of boundary
conditions. For free boundary conditions, they also depend on the coupling
strength with the heat baths. Moreover, we find a strong violation of local
equilibrium at the chain edges that determine two boundary layers of size
(where is the chain length), that are characterized by a
different scaling behaviour from the bulk. Finally, we investigate the
relaxation towards the stationary state, finding two long time scales: the
first corresponds to the relaxation of the hydrodynamic modes; the second is a
manifestation of the finiteness of the system.Comment: Submitted to Journal of Physics A, Mathematical and Theoretica
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
A stochastic model of anomalous heat transport: analytical solution of the steady state
We consider a one-dimensional harmonic crystal with conservative noise, in
contact with two stochastic Langevin heat baths at different temperatures. The
noise term consists of collisions between neighbouring oscillators that
exchange their momenta, with a rate . The stationary equations for the
covariance matrix are exactly solved in the thermodynamic limit ().
In particular, we derive an analytical expression for the temperature profile,
which turns out to be independent of . Moreover, we obtain an exact
expression for the leading term of the energy current, which scales as
. Our theoretical results are finally found to be consistent
with the numerical solutions of the covariance matrix for finite .Comment: Minor changes in the text. To appear in Journal of Physics
The process of irreversible nucleation in multilayer growth. I. Failure of the mean-field approach
The formation of stable dimers on top of terraces during epitaxial growth is
investigated in detail. In this paper we focus on mean-field theory, the
standard approach to study nucleation. Such theory is shown to be unsuitable
for the present problem, because it is equivalent to considering adatoms as
independent diffusing particles. This leads to an overestimate of the correct
nucleation rate by a factor N, which has a direct physical meaning: in average,
a visited lattice site is visited N times by a diffusing adatom. The dependence
of N on the size of the terrace and on the strength of step-edge barriers is
derived from well known results for random walks. The spatial distribution of
nucleation events is shown to be different from the mean-field prediction, for
the same physical reason. In the following paper we develop an exact treatment
of the problem.Comment: 19 pages, 3 figures. To appear in Phys. Rev.
Checkerboards, stripes and corner energies in spin models with competing interactions
We study the zero temperature phase diagram of Ising spin systems in two
dimensions in the presence of competing interactions, long range
antiferromagnetic and nearest neighbor ferromagnetic of strength J. We first
introduce the notion of a "corner energy" which shows, when the
antiferromagnetic interaction decays faster than the fourth power of the
distance, that a striped state is favored with respect to a checkerboard state
when J is close to J_c, the transition to the ferromagnetic state, i.e., when
the length scales of the uniformly magnetized domains become large. Next, we
perform detailed analytic computations on the energies of the striped and
checkerboard states in the cases of antiferromagnetic interactions with
exponential decay and with power law decay r^{-p}, p>2, that depend on the
Manhattan distance instead of the Euclidean distance. We prove that the striped
phase is always favored compared to the checkerboard phase when the scale of
the ground state structure is very large. This happens for J\lesssim J_c if
p>3, and for J sufficiently large if 2<p<=3. Many of our considerations
involving rigorous bounds carry over to dimensions greater than two and to more
general short-range ferromagnetic interactions.Comment: 21 pages, 3 figure
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