878 research outputs found
Low energy chaos in the Fermi-Pasta-Ulam problem
A possibility that in the FPU problem the critical energy for chaos goes to
zero with the increase of the number of particles in the chain is discussed.
The distribution for long linear waves in this regime is found and an estimate
for new border of transition to energy equipartition is given.Comment: revtex, 12 pages, 5 figures, submitted to Nonlinearit
Asymptotic Statistics of Poincar\'e Recurrences in Hamiltonian Systems with Divided Phase Space
By different methods we show that for dynamical chaos in the standard map
with critical golden curve the Poincar\'e recurrences P(\tau) and correlations
C(\tau) asymptotically decay in time as P ~ C/\tau ~ 1/\tau^3. It is also
explained why this asymptotic behavior starts only at very large times. We
argue that the same exponent p=3 should be also valid for a general chaos
border.Comment: revtex, 4 pages, 3 ps-figure
Universal diffusion near the golden chaos border
We study local diffusion rate in Chirikov standard map near the critical
golden curve. Numerical simulations confirm the predicted exponent
for the power law decay of as approaching the golden curve via principal
resonances with period (). The universal
self-similar structure of diffusion between principal resonances is
demonstrated and it is shown that resonances of other type play also an
important role.Comment: 4 pages Latex, revtex, 3 uuencoded postscript figure
Clustering, Chaos and Crisis in a Bailout Embedding Map
We study the dynamics of inertial particles in two dimensional incompressible
flows. The particle dynamics is modelled by four dimensional dissipative
bailout embedding maps of the base flow which is represented by 2-d area
preserving maps. The phase diagram of the embedded map is rich and interesting
both in the aerosol regime, where the density of the particle is larger than
that of the base flow, as well as the bubble regime, where the particle density
is less than that of the base flow. The embedding map shows three types of
dynamic behaviour, periodic orbits, chaotic structures and mixed regions. Thus,
the embedding map can target periodic orbits as well as chaotic structures in
both the aerosol and bubble regimes at certain values of the dissipation
parameter. The bifurcation diagram of the 4-d map is useful for the
identification of regimes where such structures can be found. An attractor
merging and widening crisis is seen for a special region for the aerosols. At
the crisis, two period-10 attractors merge and widen simultaneously into a
single chaotic attractor. Crisis induced intermittency is seen at some points
in the phase diagram. The characteristic times before bursts at the crisis show
power law behaviour as functions of the dissipation parameter. Although the
bifurcation diagram for the bubbles looks similar to that of aerosols, no such
crisis regime is seen for the bubbles. Our results can have implications for
the dynamics of impurities in diverse application contexts.Comment: 16 pages, 9 figures, submitted for publicatio
Delocalization induced by nonlinearity in systems with disorder
We study numerically the effects of nonlinearity on the Anderson localization
in lattices with disorder in one and two dimensions. The obtained results show
that at moderate strength of nonlinearity an unlimited spreading over the
lattice in time takes place with an algebraic growth of number of populated
sites . The numerical values of are found to be
approximately and 0.25 for the dimension and 2 respectively
being in a satisfactory agreement with the theoretical value . The
localization is preserved below a certain critical value of nonlinearity. We
also discuss the properties of the fidelity decay induced by a perturbation of
nonlinear field.Comment: 8 pages, 13 figures. New data and references added. Research at
http://www.quantware.ups-tlse.fr
Quantum Poincar\'e Recurrences
We show that quantum effects modify the decay rate of Poincar\'e recurrences
P(t) in classical chaotic systems with hierarchical structure of phase space.
The exponent p of the algebraic decay P(t) ~ 1/t^p is shown to have the
universal value p=1 due to tunneling and localization effects. Experimental
evidence of such decay should be observable in mesoscopic systems and cold
atoms.Comment: revtex, 4 pages, 4 figure
Manifestation of the Arnol'd Diffusion in Quantum Systems
We study an analog of the classical Arnol'd diffusion in a quantum system of
two coupled non-linear oscillators one of which is governed by an external
periodic force with two frequencies. In the classical model this very weak
diffusion happens in a narrow stochastic layer along the coupling resonance,
and leads to an increase of total energy of the system. We show that the
quantum dynamics of wave packets mimics, up to some extent, global properties
of the classical Arnol'd diffusion. This specific diffusion represents a new
type of quantum dynamics, and may be observed, for example, in 2D semiconductor
structures (quantum billiards) perturbed by time-periodic external fields.Comment: RevTex, 4 pages including 7 ps-figures, corrected forma
- …