418 research outputs found
On the scaling behavior of the abelian sandpile model
The abelian sandpile model in two dimensions does not show the type of
critical behavior familar from equilibrium systems. Rather, the properties of
the stationary state follow from the condition that an avalanche started at a
distance r from the system boundary has a probability proportional to 1/sqrt(r)
to reach the boundary. As a consequence, the scaling behavior of the model can
be obtained from evaluating dissipative avalanches alone, allowing not only to
determine the values of all exponents, but showing also the breakdown of
finite-size scaling.Comment: 4 pages, 5 figures; the new version takes into account that the
radius distribution of avalanches cannot become steeper than a certain power
la
Persistence in a Stationary Time-series
We study the persistence in a class of continuous stochastic processes that
are stationary only under integer shifts of time. We show that under certain
conditions, the persistence of such a continuous process reduces to the
persistence of a corresponding discrete sequence obtained from the measurement
of the process only at integer times. We then construct a specific sequence for
which the persistence can be computed even though the sequence is
non-Markovian. We show that this may be considered as a limiting case of
persistence in the diffusion process on a hierarchical lattice.Comment: 8 pages revte
Scaling fields in the two-dimensional abelian sandpile model
We consider the isotropic two-dimensional abelian sandpile model from a
perspective based on two-dimensional (conformal) field theory. We compute
lattice correlation functions for various cluster variables (at and off
criticality), from which we infer the field-theoretic description in the
scaling limit. We find a perfect agreement with the predictions of a c=-2
conformal field theory and its massive perturbation, thereby providing direct
evidence for conformal invariance and more generally for a description in terms
of a local field theory. The question of the height 2 variable is also
addressed, with however no definite conclusion yet.Comment: 22 pages, 1 figure (eps), uses revte
Isotropy Properties of the Multi-Step Markov Symbolic Sequences
A new object of the probability theory, the two-sided chain of symbols
(introduced in Ref. arXiv:physics/0306170) is used to study isotropy properties
of binary multi-step Markov chains with the long-range correlations.
Established statistical correspondence between the Markov chains and certain
two-sided sequences allows us to prove the isotropy properties of three classes
of the Markov chains. One of them is the important class of weakly correlated
additive Markov chains, which turned out to be equivalent to the additive
two-sided sequences.Comment: 7 page
Renormalization group approach to an Abelian sandpile model on planar lattices
One important step in the renormalization group (RG) approach to a lattice
sandpile model is the exact enumeration of all possible toppling processes of
sandpile dynamics inside a cell for RG transformations. Here we propose a
computer algorithm to carry out such exact enumeration for cells of planar
lattices in RG approach to Bak-Tang-Wiesenfeld sandpile model [Phys. Rev. Lett.
{\bf 59}, 381 (1987)] and consider both the reduced-high RG equations proposed
by Pietronero, Vespignani, and Zapperi (PVZ) [Phys. Rev. Lett. {\bf 72}, 1690
(1994)] and the real-height RG equations proposed by Ivashkevich [Phys. Rev.
Lett. {\bf 76}, 3368 (1996)]. Using this algorithm we are able to carry out RG
transformations more quickly with large cell size, e.g. cell for
the square (sq) lattice in PVZ RG equations, which is the largest cell size at
the present, and find some mistakes in a previous paper [Phys. Rev. E {\bf 51},
1711 (1995)]. For sq and plane triangular (pt) lattices, we obtain the only
attractive fixed point for each lattice and calculate the avalanche exponent
and the dynamical exponent . Our results suggest that the increase of
the cell size in the PVZ RG transformation does not lead to more accurate
results. The implication of such result is discussed.Comment: 29 pages, 6 figure
Anisotropic low field behavior and the observation of flux jumps in CeCoIn5
The magnetic behavior of the heavy fermion superconductor CeCoIn5 has been
investigated. The low field magnetization data show flux jumps in the mixed
state of the superconducting phase in a restricted range of temperature. These
flux jumps begin to disappear below 1.7 K, and are completely absent at 1.5 K.
The magnetization loops are asymmetric, suggesting that surface and geometrical
factors dominate the pinning in this system. The lower critical field (Hc1),
obtained from the magnetization data, shows a linear temperature dependence and
is anisotropic. The calculated penetration depth is also anisotropic, which is
consistent with the observation of an anisotropic superconducting gap in
CeCoIn5. The critical currents, determined from the high field isothermal
magnetization loops, are comparatively low (around 4000 A/cm2 at 1.6 K and 5
kOe).Comment: 4 pages 3 figure
Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State
A recent conjecture regarding the average of the minimum eigenvalue of the
reduced density matrix of a random complex state is proved. In fact, the full
distribution of the minimum eigenvalue is derived exactly for both the cases of
a random real and a random complex state. Our results are relevant to the
entanglement properties of eigenvectors of the orthogonal and unitary ensembles
of random matrix theory and quantum chaotic systems. They also provide a rare
exactly solvable case for the distribution of the minimum of a set of N {\em
strongly correlated} random variables for all values of N (and not just for
large N).Comment: 13 pages, 2 figures included; typos corrected; to appear in J. Stat.
Phy
Coupled channel description of 16O+142,144,146Nd scattering around the Coulomb barrier using a complex microscopic potential
Angular distributions of elastic scattering and inelastic scattering from 2+ 1 state are measured for 16O+142,144,146Nd systems at several energies in the vicinity of the Coulomb barrier. The angular distributions are systematically analyzed in coupled channel framework. Renormalized double folded real optical and coupling potentials with DDM3Y interaction have been used in the calculation. Relevant nuclear densities needed to generate the potentials are derived from shell model wavefunctions. A truncated shell model calculation has been performed and the calculated energy levels are compared with the experimental ones. To simulate the absorption, a 'hybrid' approach is adopted. The contribution to the imaginary potential of couplings to the inelastic channels, other than the 2+ 1 target excitation channel, is calculated in the Feshbach formalism. This calculated imaginary potential along with a short ranged volume Woods-Saxon potential to simulate the absorption in fusion channel reproduces the angular distributions for 16O+146Nd quite well. But for 16O+142,144Nd systems additional surface absorption is found to be necessary to fit the angular distribution data. The variations of this additional absorption term with incident energy and the mass of the target are explored. Ă© 2003 Elsevier Science B.V. All rights reserved
Self-Organized Branching Processes: A Mean-Field Theory for Avalanches
We discuss mean-field theories for self-organized criticality and the
connection with the general theory of branching processes. We point out that
the nature of the self-organization is not addressed properly by the previously
proposed mean-field theories. We introduce a new mean-field model that
explicitly takes the boundary conditions into account; in this way, the local
dynamical rules are coupled to a global equation that drives the control
parameter to its critical value. We study the model numerically, and
analytically we compute the avalanche distributions.Comment: 4 pages + 4 ps figure
Avalanches and the Renormalization Group for Pinned Charge-Density Waves
The critical behavior of charge-density waves (CDWs) in the pinned phase is
studied for applied fields increasing toward the threshold field, using
recently developed renormalization group techniques and simulations of
automaton models. Despite the existence of many metastable states in the pinned
state of the CDW, the renormalization group treatment can be used successfully
to find the divergences in the polarization and the correlation length, and, to
first order in an expansion, the diverging time scale. The
automaton models studied are a charge-density wave model and a ``sandpile''
model with periodic boundary conditions; these models are found to have the
same critical behavior, associated with diverging avalanche sizes. The
numerical results for the polarization and the diverging length and time scales
in dimensions are in agreement with the analytical treatment. These
results clarify the connections between the behaviour above and below
threshold: the characteristic correlation lengths on both sides of the
transition diverge with different exponents. The scaling of the distribution of
avalanches on the approach to threshold is found to be different for automaton
and continuous-variable models.Comment: 29 pages, 11 postscript figures included, REVTEX v3.0 (dvi and PS
files also available by anonymous ftp from external.nj.nec.com in directory
/pub/alan/cdwfigs
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