384 research outputs found
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
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.
Four-loop splitting functions in QCD -- The gluon-to-quark case
We have computed the even- moments of the gluon-to-quark
splitting function at the fourth order of perturbative QCD via the
renormalization of off-shell operator matrix elements. Our results, derived
analytically for a general gauge group, agree with all results obtained for
this function so far, in particular with the lowest five moments obtained via
physical cross sections. Using our new moments and all available endpoint
constraints, we construct approximations for the four-loop that
should be sufficient for a wide range of collider-physics applications. The
NLO corrections resulting from these and the corresponding quark-quark
splitting functions lead to a marked improvement of the perturbative accuracy
for the scale derivative of the singlet quark distribution, with effects of 1%
or less at at a standard reference scale with .Comment: 17 pages latex, 3 figures, 2 ancillary files (FORM file with results
and FORTRAN subroutine
Four-loop splitting functions in QCD -- The quark-quark case
We have computed the even- moments of the pure-singlet quark
splitting function at the fourth order of perturbative QCD via
the anomalous dimensions of off-shell flavour-singlet operator matrix elements.
Our results, derived analytically for a general gauge group, agree with all
results obtained for this function so far, in particular with the lowest six
even moments obtained via physical cross sections. Using these results and all
available endpoint constraints, we construct approximations for at
four loops that should be sufficient for most collider-physics applications.
Together with the known results for the non-singlet splitting function at this order, this effectively completes the quark-quark
contribution for the evolution of parton distribution at NLO
accuracy. Our new results thus provide a major step towards fully consistent
NLO calculations at the LHC and the reduction of the residual
uncertainty in the parton evolution to the percent level.Comment: 17 pages latex, 2 figures, 2 ancillary files (FORM file with results
and FORTRAN subroutine
Boltzmann entropy and chaos in a large assembly of weakly interacting systems
We introduce a high dimensional symplectic map, modeling a large system
consisting of weakly interacting chaotic subsystems, as a toy model to analyze
the interplay between single-particle chaotic dynamics and particles
interactions in thermodynamic systems. We study the growth with time of the
Boltzmann entropy, S_B, in this system as a function of the coarse graining
resolution. We show that a characteristic scale emerges, and that the behavior
of S_B vs t, at variance with the Gibbs entropy, does not depend on the coarse
graining resolution, as far as it is finer than this scale. The interaction
among particles is crucial to achieve this result, while the rate of entropy
growth depends essentially on the single-particle chaotic dynamics (for t not
too small). It is possible to interpret the basic features of the dynamics in
terms of a suitable Markov approximation.Comment: 21 pages, 11 figures, submitted to Journal of Statistical Physic
Numerical Observation of a Tubular Phase in Anisotropic Membranes
We provide the first numerical evidence for the existence of a tubular phase,
predicted by Radzihovsky and Toner (RT), for anisotropic tethered membranes
without self-avoidance. Incorporating anisotropy into the bending rigidity of a
simple model of a tethered membrane with free boundary conditions, we show that
the model indeed has two phase transitions corresponding to the flat-to-tubular
and tubular-to-crumpled transitions. For the tubular phase we measure the Flory
exponent and the roughness exponent . We find
and , which are in reasonable agreement with the theoretical
predictions of RT --- and .Comment: 8 pages, LaTeX, REVTEX, final published versio
Two dimensional SU(N)xSU(N) Chiral Models on the Lattice (II): the Green's Function
Analytical and numerical methods are applied to principal chiral models on a
two-dimensional lattice and their predictions are tested and compared. New
techniques for the strong coupling expansion of SU(N) models are developed and
applied to the evaluation of the two-point correlation function. The
momentum-space lattice propagator is constructed with precision O(\beta^{10})
and an evaluation of the correlation length is obtained for several different
definitions. Three-loop weak coupling contributions to the internal energy and
to the lattice and functions are evaluated for all N, and the
effect of adopting the ``energy'' definition of temperature is computed with
the same precision. Renormalization-group improved predictions for the
two-point Green's function in the weak coupling ( continuum ) regime are
obtained and successfully compared with Monte Carlo data. We find that strong
coupling is predictive up to a point where asymptotic scaling in the energy
scheme is observed. Continuum physics is insensitive to the effects of the
large N phase transition occurring in the lattice model. Universality in N is
already well established for and the large N physics is well
described by a ``hadronization'' picture.Comment: Revtex, 37 pages, 16 figures available on request by FAX or mai
Electromagnetic Form Factors with FLIC fermions
The Fat-Link Irrelevant Clover (FLIC) fermion action provides a new form of
nonperturbative O(a) improvement and allows efficient access to the light
quark-mass regime. FLIC fermions enable the construction of the
nonperturbatively O(a)-improved conserved vector current without the
difficulties associated with the fine tuning of the improvement coefficients.
The simulations are performed with an O(a^2) mean-field improved
plaquette-plus-rectangle gluon action on a 20^3 x 40 lattice with a lattice
spacing of 0.128 fm, enabling the first simulation of baryon form factors at
light quark masses on a large volume lattice.
Magnetic moments, electric charge radii and magnetic radii are extracted from
these form factors, and show interesting chiral nonanalytic behavior in the
light quark mass regime.Comment: Presented by J.Zanotti at the Workshop on Lattice Hadron Physics,
Cairns, Australia, 2003. 7pp, 8 figure
Library Design in Combinatorial Chemistry by Monte Carlo Methods
Strategies for searching the space of variables in combinatorial chemistry
experiments are presented, and a random energy model of combinatorial chemistry
experiments is introduced. The search strategies, derived by analogy with the
computer modeling technique of Monte Carlo, effectively search the variable
space even in combinatorial chemistry experiments of modest size. Efficient
implementations of the library design and redesign strategies are feasible with
current experimental capabilities.Comment: 5 pages, 3 figure
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
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