945 research outputs found
Infinite Invariant Density Determines Statistics of Time Averages for Weak Chaos
Weakly chaotic non-linear maps with marginal fixed points have an infinite
invariant measure. Time averages of integrable and non-integrable observables
remain random even in the long time limit. Temporal averages of integrable
observables are described by the Aaronson-Darling-Kac theorem. We find the
distribution of time averages of non-integrable observables, for example the
time average position of the particle. We show how this distribution is related
to the infinite invariant density. We establish four identities between
amplitude ratios controlling the statistics of the problem.Comment: 5 pages, 3 figure
Linear Response in Complex Systems: CTRW and the Fractional Fokker-Planck Equations
We consider the linear response of systems modelled by continuous-time random
walks (CTRW) and by fractional Fokker-Planck equations under the influence of
time-dependent external fields. We calculate the corresponding response
functions explicitely. The CTRW curve exhibits aging, i.e. it is not
translationally invariant in the time-domain. This is different from what
happens under fractional Fokker-Planck conditions
A highly optimized vectorized code for Monte Carlo simulations of SU(3) lattice gauge theories
New methods are introduced for improving the performance of the vectorized Monte Carlo SU(3) lattice gauge theory algorithm using the CDC CYBER 205. Structure, algorithm and programming considerations are discussed. The performance achieved for a 16(4) lattice on a 2-pipe system may be phrased in terms of the link update time or overall MFLOPS rates. For 32-bit arithmetic, it is 36.3 microsecond/link for 8 hits per iteration (40.9 microsecond for 10 hits) or 101.5 MFLOPS
Non-Poisson processes: regression to equilibrium versus equilibrium correlation functions
We study the response to perturbation of non-Poisson dichotomous fluctuations
that generate super-diffusion. We adopt the Liouville perspective and with it a
quantum-like approach based on splitting the density distribution into a
symmetric and an anti-symmetric component. To accomodate the equilibrium
condition behind the stationary correlation function, we study the time
evolution of the anti-symmetric component, while keeping the symmetric
component at equilibrium. For any realistic form of the perturbed distribution
density we expect a breakdown of the Onsager principle, namely, of the property
that the subsequent regression of the perturbation to equilibrium is identical
to the corresponding equilibrium correlation function. We find the directions
to follow for the calculation of higher-order correlation functions, an
unsettled problem, which has been addressed in the past by means of
approximations yielding quite different physical effects.Comment: 30 page
Coherent Destruction of Photon Emission from a Single Molecule Source
The behavior of a single molecule driven simultaneously by a laser and by an
electric radio frequency field is investigated using a non-Hermitian
Hamiltonian approach. Employing the renormalization group method for
differential equations we calculate the average waiting time for the first
photon emission event to occur, and determine the conditions for the
suppression and enhancement of photon emission. An abrupt transition from
localization-like behavior to delocalization behavior is found.Comment: 5 pages, 4 figure
Stochastic Ergodicity Breaking: a Random Walk Approach
The continuous time random walk (CTRW) model exhibits a non-ergodic phase
when the average waiting time diverges. Using an analytical approach for the
non-biased and the uniformly biased CTRWs, and numerical simulations for the
CTRW in a potential field, we obtain the non-ergodic properties of the random
walk which show strong deviations from Boltzmann--Gibbs theory. We derive the
distribution function of occupation times in a bounded region of space which,
in the ergodic phase recovers the Boltzmann--Gibbs theory, while in the
non-ergodic phase yields a generalized non-ergodic statistical law.Comment: 5 pages, 3 figure
Towards deterministic equations for Levy walks: the fractional material derivative
Levy walks are random processes with an underlying spatiotemporal coupling.
This coupling penalizes long jumps, and therefore Levy walks give a proper
stochastic description for a particle's motion with broad jump length
distribution. We derive a generalized dynamical formulation for Levy walks in
which the fractional equivalent of the material derivative occurs. Our approach
will be useful for the dynamical formulation of Levy walks in an external force
field or in phase space for which the description in terms of the continuous
time random walk or its corresponding generalized master equation are less well
suited
Ergodicity Breaking in a Deterministic Dynamical System
The concept of weak ergodicity breaking is defined and studied in the context
of deterministic dynamics. We show that weak ergodicity breaking describes a
weakly chaotic dynamical system: a nonlinear map which generates subdiffusion
deterministically. In the non-ergodic phase non-trivial distribution of the
fraction of occupation times is obtained. The visitation fraction remains
uniform even in the non-ergodic phase. In this sense the non-ergodicity is
quantified, leading to a statistical mechanical description of the system even
though it is not ergodic.Comment: 11 pages, 4 figure
Analytical and Numerical Study of Internal Representations in Multilayer Neural Networks with Binary Weights
We study the weight space structure of the parity machine with binary weights
by deriving the distribution of volumes associated to the internal
representations of the learning examples. The learning behaviour and the
symmetry breaking transition are analyzed and the results are found to be in
very good agreement with extended numerical simulations.Comment: revtex, 20 pages + 9 figures, to appear in Phys. Rev.
- …