74 research outputs found
The production rate of the coarse grained Gibbs entropy and the Kolmogorov-Sinai entropy: a real connection ?
We discuss the connection between the Kolmogorov-Sinai entropy, , and
the production rate of the coarse grained Gibbs entropy, . Detailed
numerical computations show that the (often accepted) identification of the two
quantities does not hold in systems with intermittent behavior and/or very
different characteristic times and in systems presenting pseudo-chaos. The
basic reason of this fact is in the asymptotic (with respect to time) nature of
, while is a quantity related to short time features of a system.Comment: 8 pages, 5 figures Submitted to PR
Properties making a chaotic system a good Pseudo Random Number Generator
We discuss two properties making a deterministic algorithm suitable to
generate a pseudo random sequence of numbers: high value of Kolmogorov-Sinai
entropy and high-dimensionality. We propose the multi dimensional Anosov
symplectic (cat) map as a Pseudo Random Number Generator. We show what chaotic
features of this map are useful for generating Pseudo Random Numbers and
investigate numerically which of them survive in the discrete version of the
map. Testing and comparisons with other generators are performed.Comment: 10 pages, 3 figures, new version, title changed and minor correction
Scaling and topology in the 2-d O(3) -model on the lattice with the fixed point action
We study scaling properties and topological aspects of the 2--d O(3)
non--linear --model on the lattice with the parametrized fixed point
action recently proposed by P.~Hasenfratz and F.~Niedermayer. The behavior of
the mass gap confirms the good properties of scaling of the fixed point action.
Concerning the topology, lattice classical solutions are proved to be very
stable under local minimization of the action; this outcome ensures the
reliability of the cooling method for the computation of the topological
susceptibility, which indeed reproduces the results of the field theoretical
approach. Disagreement is instead observed with a different approach in which
the fixed point topological charge operator is used: we argue that the
discrepancy is related to the ultraviolet dominated nature of the model.Comment: 24 pages (Latex) + 8 figures (PostScript) in a uuencoded compressed
tar fil
A strong-coupling analysis of two-dimensional O(N) sigma models with on square, triangular and honeycomb lattices
Recently-generated long strong-coupling series for the two-point Green's
functions of asymptotically free lattice models are
analyzed, focusing on the evaluation of dimensionless renormalization-group
invariant ratios of physical quantities and applying resummation techniques to
series in the inverse temperature and in the energy . Square,
triangular, and honeycomb lattices are considered, as a test of universality
and in order to estimate systematic errors. Large- solutions are carefully
studied in order to establish benchmarks for series coefficients and
resummations. Scaling and universality are verified. All invariant ratios
related to the large-distance properties of the two-point functions vary
monotonically with , departing from their large- values only by a few per
mille even down to .Comment: 53 pages (incl. 5 figures), tar/gzip/uuencode, REVTEX + psfi
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