3,407 research outputs found
Chaotic itinerancy and power-law residence time distribution in stochastic dynamical system
To study a chaotic itinerant motion among varieties of ordered states, we
propose a stochastic model based on the mechanism of chaotic itinerancy. The
model consists of a random walk on a half-line, and a Markov chain with a
transition probability matrix. To investigate the stability of attractor ruins
in the model, we analyze the residence time distribution of orbits at attractor
ruins. We show that the residence time distribution averaged by all attractor
ruins is given by the superposition of (truncated) power-law distributions, if
a basin of attraction for each attractor ruin has zero measure. To make sure of
this result, we carry out a computer simulation for models showing chaotic
itinerancy. We also discuss the fact that chaotic itinerancy does not occur in
coupled Milnor attractor systems if the transition probability among attractor
ruins can be represented as a Markov chain.Comment: 6 pages, 10 figure
A Random Walk to a Non-Ergodic Equilibrium Concept
Random walk models, such as the trap model, continuous time random walks, and
comb models exhibit weak ergodicity breaking, when the average waiting time is
infinite. The open question is: what statistical mechanical theory replaces the
canonical Boltzmann-Gibbs theory for such systems? In this manuscript a
non-ergodic equilibrium concept is investigated, for a continuous time random
walk model in a potential field. In particular we show that in the non-ergodic
phase the distribution of the occupation time of the particle on a given
lattice point, approaches U or W shaped distributions related to the arcsin
law. We show that when conditions of detailed balance are applied, these
distributions depend on the partition function of the problem, thus
establishing a relation between the non-ergodic dynamics and canonical
statistical mechanics. In the ergodic phase the distribution function of the
occupation times approaches a delta function centered on the value predicted
based on standard Boltzmann-Gibbs statistics. Relation of our work with single
molecule experiments is briefly discussed.Comment: 14 pages, 6 figure
Discrete Spectra of Semirelativistic Hamiltonians
We review various attempts to localize the discrete spectra of
semirelativistic Hamiltonians of the form H = \beta \sqrt{m^2 + p^2} + V(r)
(w.l.o.g. in three spatial dimensions) as entering, for instance, in the
spinless Salpeter equation. Every Hamiltonian in this class of operators
consists of the relativistic kinetic energy \beta \sqrt{m^2 + p^2} (where \beta
> 0 allows for the possibility of more than one particles of mass m) and a
spherically symmetric attractive potential V(r), r = |x|. In general, accurate
eigenvalues of a nonlocal Hamiltonian operator can only be found by the use of
a numerical approximation procedure. Our main emphasis, however, is on the
derivation of rigorous semi-analytical expressions for both upper and lower
bounds to the energy levels of such operators. We compare the bounds obtained
within different approaches and present relationships existing between the
bounds.Comment: 21 pages, 3 figure
Equilibrium of anchored interfaces with quenched disordered growth
The roughening behavior of a one-dimensional interface fluctuating under
quenched disorder growth is examined while keeping an anchored boundary. The
latter introduces detailed balance conditions which allows for a thorough
analysis of equilibrium aspects at both macroscopic and microscopic scales. It
is found that the interface roughens linearly with the substrate size only in
the vicinity of special disorder realizations. Otherwise, it remains stiff and
tilted.Comment: 6 pages, 3 postscript figure
Small violations of full correlation Bell inequalities for multipartite pure random states
We estimate the probability of random -qudit pure states violating
full-correlation Bell inequalities with two dichotomic observables per site.
These inequalities can show violations that grow exponentially with , but we
prove this is not the typical case. For many-qubit states the probability to
violate any of these inequalities by an amount that grows linearly with is
vanishingly small. If each system's Hilbert space dimension is larger than two,
on the other hand, the probability of seeing \emph{any} violation is already
small. For the qubits case we discuss furthermore the consequences of this
result for the probability of seeing arbitrary violations (\emph i.e., of any
order of magnitude) when experimental imperfections are considered.Comment: 16 pages, one colum
From laser cooling to aging: a unified Levy flight description
Intriguing phenomena such as subrecoil laser cooling of atoms, or aging
phenomenon in glasses, have in common that the systems considered do not reach
a steady-state during the experiments, although the experimental time scales
are very large compared to the microscopic ones. We revisit some standard
models describing these phenomena, and reformulate them in a unified framework
in terms of lifetimes of the microscopic states of the system. A universal
dynamical mechanism emerges, leading to a generic time-dependent distribution
of lifetimes, independently of the physical situation considered.Comment: 8 pages, 2 figures; accepted for publication in American Journal of
Physic
Dephasing by a nonstationary classical intermittent noise
We consider a new phenomenological model for a classical
intermittent noise and study its effects on the dephasing of a two-level
system. Within this model, the evolution of the relative phase between the
states is described as a continuous time random walk (CTRW). Using
renewal theory, we find exact expressions for the dephasing factor and identify
the physically relevant various regimes in terms of the coupling to the noise.
In particular, we point out the consequences of the non-stationarity and
pronounced non-Gaussian features of this noise, including some new anomalous
and aging dephasing scenarii.Comment: Submitted to Phys. Rev.
Fractal time random walk and subrecoil laser cooling considered as renewal processes with infinite mean waiting times
There exist important stochastic physical processes involving infinite mean
waiting times. The mean divergence has dramatic consequences on the process
dynamics. Fractal time random walks, a diffusion process, and subrecoil laser
cooling, a concentration process, are two such processes that look
qualitatively dissimilar. Yet, a unifying treatment of these two processes,
which is the topic of this pedagogic paper, can be developed by combining
renewal theory with the generalized central limit theorem. This approach
enables to derive without technical difficulties the key physical properties
and it emphasizes the role of the behaviour of sums with infinite means.Comment: 9 pages, 7 figures, to appear in the Proceedings of Cargese Summer
School on "Chaotic dynamics and transport in classical and quantum systems
Motional Broadening in Ensembles With Heavy-Tail Frequency Distribution
We show that the spectrum of an ensemble of two-level systems can be
broadened through `resetting' discrete fluctuations, in contrast to the
well-known motional-narrowing effect. We establish that the condition for the
onset of motional broadening is that the ensemble frequency distribution has
heavy tails with a diverging first moment. We find that the asymptotic
motional-broadened lineshape is a Lorentzian, and derive an expression for its
width. We explain why motional broadening persists up to some fluctuation rate,
even when there is a physical upper cutoff to the frequency distribution.Comment: 6 pages, 4 figure
Ballistic Annihilation Kinetics: The Case of Discrete Velocity Distributions
The kinetics of the annihilation process, , with ballistic particle
motion is investigated when the distribution of particle velocities is {\it
discrete}. This discreteness is the source of many intriguing phenomena. In the
mean field limit, the densities of different velocity species decay in time
with different power law rates for many initial conditions. For a
one-dimensional symmetric system containing particles with velocity 0 and , there is a particular initial state for which the concentrations of all
three species as decay as . For the case of a fast ``impurity'' in a
symmetric background of and particles, the impurity survival
probability decays as . In a symmetric
4-velocity system in which there are particles with velocities and
, there again is a special initial condition where the two species
decay at the same rate, t^{-\a}, with \a\cong 0.72. Efficient algorithms
are introduced to perform the large-scale simulations necessary to observe
these unusual phenomena clearly.Comment: 18 text pages, macro file included, hardcopy of 9 figures available
by email request to S
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