635 research outputs found
Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators
Chaos synchronization in a ring of diffusively coupled nonlinear oscillators
driven by an external identical oscillator is studied. Based on numerical
simulations we show that by introducing additional couplings at -th
oscillators in the ring, where is an integer and is the maximum
number of synchronized oscillators in the ring with a single coupling, the
maximum number of oscillators that can be synchronized can be increased
considerably beyond the limit restricted by size instability. We also
demonstrate that there exists an exponential relation between the number of
oscillators that can support stable synchronization in the ring with the
external drive and the critical coupling strength with a scaling
exponent . The critical coupling strength is calculated by numerically
estimating the synchronization error and is also confirmed from the conditional
Lyapunov exponents (CLEs) of the coupled systems. We find that the same scaling
relation exists for couplings between the drive and the ring. Further, we
have examined the robustness of the synchronous states against Gaussian white
noise and found that the synchronization error exhibits a power-law decay as a
function of the noise intensity indicating the existence of both noise-enhanced
and noise-induced synchronizations depending on the value of the coupling
strength . In addition, we have found that shows an
exponential decay as a function of the number of additional couplings. These
results are demonstrated using the paradigmatic models of R\"ossler and Lorenz
oscillators.Comment: Accepted for Publication in Physical Review
Integrable theory of quantum transport in chaotic cavities
The problem of quantum transport in chaotic cavities with broken
time-reversal symmetry is shown to be completely integrable in the universal
limit. This observation is utilised to determine the cumulants and the
distribution function of conductance for a cavity with ideal leads supporting
an arbitrary number of propagating modes. Expressed in terms of solutions
to the fifth Painlev\'e transcendent and/or the Toda lattice equation, the
conductance distribution is further analysed in the large- limit that
reveals long exponential tails in the otherwise Gaussian curve.Comment: 4 pages; final version to appear in Physical Review Letter
Effective Chiral Meson Lagrangian For The Extended Nambu-Jona-Lasinio Model
We present a derivation of the low-energy effective meson Lagrangian of the
extended Nambu -- Jona-Lasinio (ENJL) model. The case with linear realization
of broken chiral symmetry is considered. There are two
crucial points why this revision is needed. Firstly it is the explicit chiral
symmetry breaking effect. On the basis of symmetry arguments we show that
relevant contributions related with the current quark mass terms are absent
from the effective Lagrangians derived so far in the literature. Secondly we
suggest a chiral covariant way to avoid non-diagonal terms responsible for the
pseudoscalar -- axial-vector mixing from the effective meson Lagrangian. In the
framework of the linear approach this diagonalization has not been done
correctly. We discuss as well the coset space
parametrization for the revised Lagrangian (nonlinear ansatz). Our Lagrangian
differs in an essential way from those that have been derived till now on the
basis of both linear and nonlinear realizations of chiral symmetry.Comment: 23 pages, plain LaTex, no figure
Scenarios of domain pattern formation in a reaction-diffusion system
We performed an extensive numerical study of a two-dimensional
reaction-diffusion system of the activator-inhibitor type in which domain
patterns can form. We showed that both multidomain and labyrinthine patterns
may form spontaneously as a result of Turing instability. In the stable
homogeneous system with the fast inhibitor one can excite both localized and
extended patterns by applying a localized stimulus. Depending on the parameters
and the excitation level of the system stripes, spots, wriggled stripes, or
labyrinthine patterns form. The labyrinthine patterns may be both connected and
disconnected. In the the stable homogeneous system with the slow inhibitor one
can excite self-replicating spots, breathing patterns, autowaves and
turbulence. The parameter regions in which different types of patterns are
realized are explained on the basis of the asymptotic theory of instabilities
for patterns with sharp interfaces developed by us in Phys. Rev. E. 53, 3101
(1996). The dynamics of the patterns observed in our simulations is very
similar to that of the patterns forming in the ferrocyanide-iodate-sulfite
reaction.Comment: 15 pages (REVTeX), 15 figures (postscript and gif), submitted to
Phys. Rev.
Experimental Verification of the Chemical Sensitivity of Two-Site Double Core-Hole States Formed by an X-ray FEL
We have performed X-ray two-photon photoelectron spectroscopy (XTPPS) using
the Linac Coherent Light Source (LCLS) X-ray free-electron laser (FEL) in order
to study double core-hole (DCH) states of CO2, N2O and N2. The experiment
verifies the theory behind the chemical sensitivity of two-site (ts) DCH states
by comparing a set of small molecules with respect to the energy shift of the
tsDCH state and by extracting the relevant parameters from this shift.Comment: 11 pages, 2 figure
Entangled random pure states with orthogonal symmetry: exact results
We compute analytically the density of Schmidt
eigenvalues, distributed according to a fixed-trace Wishart-Laguerre measure,
and the average R\'enyi entropy for reduced
density matrices of entangled random pure states with orthogonal symmetry
. The results are valid for arbitrary dimensions of the
corresponding Hilbert space partitions, and are in excellent agreement with
numerical simulations.Comment: 15 pages, 5 figure
Modification of the experimental setup of the FTIR spectrometer and thirty-meter optical cell for measurements of weak selective and nonselective absorptions
The improvement of the experimental setup based on a Fourier spectrometer Bruker IFS-125 and a 30-meter multipass optical cell is described. The improvement includes the cell equipment with a system of automated adjustment of the number of beam passes without cell depressurization and ensures the cell work at high temperatures
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