635 research outputs found
Broken ergodicity and glassy behavior in a deterministic chaotic map
A network of elements is studied in terms of a deterministic globally
coupled map which can be chaotic. There exists a range of values for the
parameters of the map where the number of different macroscopic configurations
is very large, and there is violation of selfaveraging. The time averages of
functions, which depend on a single element, computed over a time , have
probability distributions that do not collapse to a delta function, for
increasing and . This happens for both chaotic and regular motion, i.e.
positive or negative Lyapunov exponent.Comment: 3 pages RevTeX 3.0, 4 figures included (postscript), files packed
with uufile
Predictability: a way to characterize Complexity
Different aspects of the predictability problem in dynamical systems are
reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy,
Shannon entropy and algorithmic complexity is discussed. In particular, we
emphasize how a characterization of the unpredictability of a system gives a
measure of its complexity. Adopting this point of view, we review some
developments in the characterization of the predictability of systems showing
different kind of complexity: from low-dimensional systems to high-dimensional
ones with spatio-temporal chaos and to fully developed turbulence. A special
attention is devoted to finite-time and finite-resolution effects on
predictability, which can be accounted with suitable generalization of the
standard indicators. The problems involved in systems with intrinsic randomness
is discussed, with emphasis on the important problems of distinguishing chaos
from noise and of modeling the system. The characterization of irregular
behavior in systems with discrete phase space is also considered.Comment: 142 Latex pgs. 41 included eps figures, submitted to Physics Reports.
Related information at this http://axtnt2.phys.uniroma1.i
The Flat Phase of Crystalline Membranes
We present the results of a high-statistics Monte Carlo simulation of a
phantom crystalline (fixed-connectivity) membrane with free boundary. We verify
the existence of a flat phase by examining lattices of size up to . The
Hamiltonian of the model is the sum of a simple spring pair potential, with no
hard-core repulsion, and bending energy. The only free parameter is the the
bending rigidity . In-plane elastic constants are not explicitly
introduced. We obtain the remarkable result that this simple model dynamically
generates the elastic constants required to stabilise the flat phase. We
present measurements of the size (Flory) exponent and the roughness
exponent . We also determine the critical exponents and
describing the scale dependence of the bending rigidity () and the induced elastic constants (). At bending rigidity , we find
(Hausdorff dimension ), and . These results are consistent with the scaling relation . The additional scaling relation implies
. A direct measurement of from the power-law decay of
the normal-normal correlation function yields on the
lattice.Comment: Latex, 31 Pages with 14 figures. Improved introduction, appendix A
and discussion of numerical methods. Some references added. Revised version
to appear in J. Phys.
Coarse-Grained Probabilistic Automata Mimicking Chaotic Systems
Discretization of phase space usually nullifies chaos in dynamical systems.
We show that if randomness is associated with discretization dynamical chaos
may survive and be indistinguishable from that of the original chaotic system,
when an entropic, coarse-grained analysis is performed. Relevance of this
phenomenon to the problem of quantum chaos is discussed.Comment: 4 pages, 4 figure
Stochastic Resonance in Deterministic Chaotic Systems
We propose a mechanism which produces periodic variations of the degree of
predictability in dynamical systems. It is shown that even in the absence of
noise when the control parameter changes periodically in time, below and above
the threshold for the onset of chaos, stochastic resonance effects appears. As
a result one has an alternation of chaotic and regular, i.e. predictable,
evolutions in an almost periodic way, so that the Lyapunov exponent is positive
but some time correlations do not decay.Comment: 9 Pages + 3 Figures, RevTeX 3.0, sub. J. Phys.
Four loop results for the 2D O(n) nonlinear sigma model with 0-loop and 1-loop Symanzik actions
We present complete three loop results and preliminary four loop results for
the 2D O(n) nonlinear sigma model with 0-loop and 1-loop Symanzik improved
actions. This calculation aims to test the improvement in the numerical
precision that the combination of Symanzik actions and effective couplings can
give in Monte Carlo simulations.Comment: LATTICE99(spin models). 3 pages, contains espcrc2.sty fil
The method of global R* and its applications
The global R* operation is a powerful method for computing renormalisation
group functions. This technique, based on the principle of infrared
rearrangement, allows to express all the ultraviolet counterterms in terms of
massless propagator integrals. In this talk we present the main features of
global R* and its application to the renormalisation of QCD. By combining this
approach with the use of the program Forcer for the evaluation of the relevant
Feynman integrals, we renormalise for the first time QCD at five loops in
covariant gauges.Comment: 10 pages, 6 figures, contribution to the proceedings of the 13th
International Symposium on Radiative Corrections (RADCOR 2017
Two dimensional SU(N) x SU(N) chiral models on the lattice
Lattice chiral models are analyzed by strong and weak
coupling expansions and by numerical simulations. order strong
coupling series for the free and internal energy are obtained for all . Three loop contributions to the internal energy and to the lattice
-function are evaluated for all and non-universal corrections to the
asymptotic parameter are computed in the ``temperature'' and the
``energy'' scheme. Numerical simulations confirm a faster approach to
asymptopia of the energy scheme. A phenomenological correlation between the
peak in the specific heat and the dip of the -function is observed.
Tests of scaling are performed for various physical quantities, finding
substantial scaling at . In particular, at three different
mass ratios are determined numerically and found in agreement, within
statistical errors of about 1\%, with the theoretical predictions from the
exact S-matrix theory.Comment: pre-print IFUP 29/93, revised version, 12 pages, 10 figures avaliable
on request by FAX or by mail. REVTE
One-dimensional asymmetrically coupled maps with defects
In this letter we study chaotic dynamical properties of an asymmetrically
coupled one-dimensional chain of maps. We discuss the existence of coherent
regions in terms of the presence of defects along the chain. We find out that
temporal chaos is instantaneously localized around one single defect and that
the tangent vector jumps from one defect to another in an apparently random
way. We quantitatively measure the localization properties by defining an
entropy-like function in the space of tangent vectors.Comment: 9 pages + 4 figures TeX dialect: Plain TeX + IOP macros (included
Generalised Spin Projection for Fermion Actions
The majority of compute time doing lattice QCD is spent inverting the fermion
matrix. The time that this takes increases with the condition number of the
matrix. The FLIC(Fat Link Irrelevant Clover) action displays, among other
properties, an improved condition number compared to standard actions and hence
is of interest due to potential compute time savings. However, due to its two
different link sets there is a factor of two cost in floating point
multiplications compared to the Wilson action. An additional factor of two has
been attributed due to the loss of the so-called spin projection trick. We show
that any split-link action may be written in terms of spin projectors, reducing
the additional cost to at most a factor of two. Also, we review an efficient
means of evaluating the clover term, which is additional expense not present in
the Wilson action.Comment: 4 page
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