2,088 research outputs found
Statistics of quantum transmission in one dimension with broad disorder
We study the statistics of quantum transmission through a one-dimensional
disordered system modelled by a sequence of independent scattering units. Each
unit is characterized by its length and by its action, which is proportional to
the logarithm of the transmission probability through this unit. Unit actions
and lengths are independent random variables, with a common distribution that
is either narrow or broad. This investigation is motivated by results on
disordered systems with non-stationary random potentials whose fluctuations
grow with distance.
In the statistical ensemble at fixed total sample length four phases can be
distinguished, according to the values of the indices characterizing the
distribution of the unit actions and lengths. The sample action, which is
proportional to the logarithm of the conductance across the sample, is found to
obey a fluctuating scaling law, and therefore to be non-self-averaging, in
three of the four phases. According to the values of the two above mentioned
indices, the sample action may typically grow less rapidly than linearly with
the sample length (underlocalization), more rapidly than linearly
(superlocalization), or linearly but with non-trivial sample-to-sample
fluctuations (fluctuating localization).Comment: 26 pages, 4 figures, 1 tabl
Surface Properties of Aperiodic Ising Quantum Chains
We consider Ising quantum chains with quenched aperiodic disorder of the
coupling constants given through general substitution rules. The critical
scaling behaviour of several bulk and surface quantities is obtained by exact
real space renormalization.Comment: 4 pages, RevTex, reference update
Competition and cooperation:aspects of dynamics in sandpiles
In this article, we review some of our approaches to granular dynamics, now
well known to consist of both fast and slow relaxational processes. In the
first case, grains typically compete with each other, while in the second, they
cooperate. A typical result of {\it cooperation} is the formation of stable
bridges, signatures of spatiotemporal inhomogeneities; we review their
geometrical characteristics and compare theoretical results with those of
independent simulations. {\it Cooperative} excitations due to local density
fluctuations are also responsible for relaxation at the angle of repose; the
{\it competition} between these fluctuations and external driving forces, can,
on the other hand, result in a (rare) collapse of the sandpile to the
horizontal. Both these features are present in a theory reviewed here. An arena
where the effects of cooperation versus competition are felt most keenly is
granular compaction; we review here a random graph model, where three-spin
interactions are used to model compaction under tapping. The compaction curve
shows distinct regions where 'fast' and 'slow' dynamics apply, separated by
what we have called the {\it single-particle relaxation threshold}. In the
final section of this paper, we explore the effect of shape -- jagged vs.
regular -- on the compaction of packings near their jamming limit. One of our
major results is an entropic landscape that, while microscopically rough,
manifests {\it Edwards' flatness} at a macroscopic level. Another major result
is that of surface intermittency under low-intensity shaking.Comment: 36 pages, 23 figures, minor correction
Dynamics at the angle of repose: jamming, bistability, and collapse
When a sandpile relaxes under vibration, it is known that its measured angle
of repose is bistable in a range of values bounded by a material-dependent
maximal angle of stability; thus, at the same angle of repose, a sandpile can
be stationary or avalanching, depending on its history. In the nearly jammed
slow dynamical regime, sandpile collapse to a zero angle of repose can also
occur, as a rare event. We claim here that fluctuations of {\it dilatancy} (or
local density) are the key ingredient that can explain such varied phenomena.
In this work, we model the dynamics of the angle of repose and of the density
fluctuations, in the presence of external noise, by means of coupled stochastic
equations. Among other things, we are able to describe sandpile collapse in
terms of an activated process, where an effective temperature (related to the
density as well as to the external vibration intensity) competes against the
configurational barriers created by the density fluctuations.Comment: 15 pages, 1 figure. Minor changes and update
Theoretical Models for Classical Cepheids: IV. Mean Magnitudes and Colors and the Evaluation of Distance, Reddening and Metallicity
We discuss the metallicity effect on the theoretical visual and near-infrared
PL and PLC relations of classical Cepheids, as based on nonlinear, nonlocal and
time--dependent convective pulsating models at varying chemical composition. In
view of the two usual methods of averaging (magnitude-weighted and
intensity-weighted) observed magnitudes and colors over the full pulsation
cycle, we briefly discuss the differences between static and mean quantities.
We show that the behavior of the synthetic mean magnitudes and colors fully
reproduces the observed trend of Galactic Cepheids, supporting the validity of
the model predictions. In the second part of the paper we show how the estimate
of the mean reddening and true distance modulus of a galaxy from Cepheid VK
photometry depend on the adopted metal content, in the sense that larger
metallicities drive the host galaxy to lower extinctions and distances.
Conversely, self-consistent estimates of the Cepheid mean reddening, distance
and metallicity may be derived if three-filter data are taken into account. By
applying the theoretical PL and PLC relations to available BVK data of Cepheids
in the Magellanic Clouds we eventually obtain Z \sim 0.008, E(B-V) \sim 0.02
mag, DM \sim 18.63 mag for LMC and Z \sim 0.004, E(B-V) \sim 0.01 mag., DM \sim
19.16 mag. for SMC. The discrepancy between such reddenings and the current
values based on BVI data is briefly discussed.Comment: 16 pages, 11 postscript figures, accepted for publication on Ap
Entanglement entropy of aperiodic quantum spin chains
We study the entanglement entropy of blocks of contiguous spins in
non-periodic (quasi-periodic or more generally aperiodic) critical Heisenberg,
XX and quantum Ising spin chains, e.g. in Fibonacci chains. For marginal and
relevant aperiodic modulations, the entanglement entropy is found to be a
logarithmic function of the block size with log-periodic oscillations. The
effective central charge, c_eff, defined through the constant in front of the
logarithm may depend on the ratio of couplings and can even exceed the
corresponding value in the homogeneous system. In the strong modulation limit,
the ground state is constructed by a renormalization group method and the
limiting value of c_eff is exactly calculated. Keeping the ratio of the block
size and the system size constant, the entanglement entropy exhibits a scaling
property, however, the corresponding scaling function may be nonanalytic.Comment: 6 pages, 2 figure
Reddenings of FGK supergiants and classical Cepheids from spectroscopic data
Accurate and homogeneous atmospheric parameters (Teff, log (g), Vt, [Fe/H])
are derived for 74 FGK non-variable supergiants from high-resolution, high
signal-to-noise ratio, echelle spectra. Extremely high precision for the
inferred effective temperatures (10-40 K) is achieved by using the line-depth
ratio method. The new data are combined with atmospheric values for 164
classical Cepheids, observed at 675 different pulsation phases, taken from our
previously published studies. The derived values are correlated with unreddened
B-V colours compiled from the literature for the investigated stars in order to
obtain an empirical relationship of the form: (B-V)o = 57.984 - 10.3587(log
Teff)^2 + 1.67572(log Teff)^3 - 3.356(log (g)) + 0.0321(Vt) + 0.2615[Fe/H] +
0.8833((log (g))(log Teff)). The expression is used to estimate colour excesses
E(B-V) for individual supergiants and classical Cepheids, with a precision of
+-0.05 mag. for supergiants and Cepheids with n=1-2 spectra, reaching +-0.025
mag. for Cepheids with n>2 spectra, matching uncertainties for the most
sophisticated photometric techniques. The reddening scale is also a close match
to the system of space reddenings for Cepheids. The application range is for
spectral types F0--K0 and luminosity classes I and II.Comment: accepted for publication (MNRAS
Structure of the stationary state of the asymmetric target process
We introduce a novel migration process, the target process. This process is
dual to the zero-range process (ZRP) in the sense that, while for the ZRP the
rate of transfer of a particle only depends on the occupation of the departure
site, it only depends on the occupation of the arrival site for the target
process. More precisely, duality associates to a given ZRP a unique target
process, and vice-versa. If the dynamics is symmetric, i.e., in the absence of
a bias, both processes have the same stationary-state product measure. In this
work we focus our interest on the situation where the latter measure exhibits a
continuous condensation transition at some finite critical density ,
irrespective of the dimensionality. The novelty comes from the case of
asymmetric dynamics, where the target process has a nontrivial fluctuating
stationary state, whose characteristics depend on the dimensionality. In one
dimension, the system remains homogeneous at any finite density. An alternating
scenario however prevails in the high-density regime: typical configurations
consist of long alternating sequences of highly occupied and less occupied
sites. The local density of the latter is equal to and their
occupation distribution is critical. In dimension two and above, the asymmetric
target process exhibits a phase transition at a threshold density much
larger than . The system is homogeneous at any density below ,
whereas for higher densities it exhibits an extended condensate elongated along
the direction of the mean current, on top of a critical background with density
.Comment: 30 pages, 16 figure
On the statistics of superlocalized states in self-affine disordered potentials
We investigate the statistics of eigenstates in a weak self-affine disordered
potential in one dimension, whose Gaussian fluctuations grow with distance with
a positive Hurst exponent . Typical eigenstates are superlocalized on
samples much larger than a well-defined crossover length, which diverges in the
weak-disorder regime. We present a parallel analytical investigation of the
statistics of these superlocalized states in the discrete and the continuum
formalisms. For the discrete tight-binding model, the effective localization
length decays logarithmically with the sample size, and the logarithm of the
transmission is marginally self-averaging. For the continuum Schr\"odinger
equation, the superlocalization phenomenon has more drastic effects. The
effective localization length decays as a power of the sample length, and the
logarithm of the transmission is fully non-self-averaging.Comment: 21 pages, 6 figure
Critical properties of an aperiodic model for interacting polymers
We investigate the effects of aperiodic interactions on the critical behavior
of an interacting two-polymer model on hierarchical lattices (equivalent to the
Migadal-Kadanoff approximation for the model on Bravais lattices), via
renormalization-group and tranfer-matrix calculations. The exact
renormalization-group recursion relations always present a symmetric fixed
point, associated with the critical behavior of the underlying uniform model.
If the aperiodic interactions, defined by s ubstitution rules, lead to relevant
geometric fluctuations, this fixed point becomes fully unstable, giving rise to
novel attractors of different nature. We present an explicit example in which
this new attractor is a two-cycle, with critical indices different from the
uniform model. In case of the four-letter Rudin-Shapiro substitution rule, we
find a surprising closed curve whose points are attractors of period two,
associated with a marginal operator. Nevertheless, a scaling analysis indicates
that this attractor may lead to a new critical universality class. In order to
provide an independent confirmation of the scaling results, we turn to a direct
thermodynamic calculation of the specific-heat exponent. The thermodynamic free
energy is obtained from a transfer matrix formalism, which had been previously
introduced for spin systems, and is now extended to the two-polymer model with
aperiodic interactions.Comment: 19 pages, 6 eps figures, to appear in J. Phys A: Math. Ge
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