55 research outputs found
Characterizing weak chaos in nonintegrable Hamiltonian systems: the fundamental role of stickiness and initial conditions
Weak chaos in high-dimensional conservative systems can be characterized
through sticky effect induced by invariant structures on chaotic trajectories.
Suitable quantities for this characterization are the higher cummulants of the
finite time Lyapunov exponents (FTLEs) distribution. They gather the {\it
whole} phase space relevant dynamics in {\it one} quantity and give
informations about ordered and random states. This is analyzed here for
discrete Hamiltonian systems with local and global couplings. It is also shown
that FTLEs plotted {\it versus} initial condition (IC) and the nonlinear
parameter is essential to understand the fundamental role of ICs in the
dynamics of weakly chaotic Hamiltonian systems.Comment: 7 pages, 6 figures, submitted for publicatio
Quantum-classical transition and quantum activation of ratchet currents in the parameter space
The quantum ratchet current is studied in the parameter space of the
dissipative kicked rotor model coupled to a zero temperature quantum
environment. We show that vacuum fluctuations blur the generic isoperiodic
stable structures found in the classical case. Such structures tend to survive
when a measure of statistical dependence between the quantum and classical
currents are displayed in the parameter space. In addition, we show that
quantum fluctuations can be used to overcome transport barriers in the phase
space. Related quantum ratchet current activation regions are spotted in the
parameter space. Results are discussed {based on quantum, semiclassical and
classical calculations. While the semiclassical dynamics involves vacuum
fluctuations, the classical map is driven by thermal noise.Comment: 6 pages, 3 figure
Decay of distance autocorrelation and Lyapunov exponents
This work presents numerical evidences that for discrete dynamical systems
with one positive Lyapunov exponent the decay of the distance autocorrelation
is always related to the Lyapunov exponent. Distinct decay laws for the
distance autocorrelation are observed for different systems, namely exponential
decays for the quadratic map, logarithmic for the H\'enon map and power-law for
the conservative standard map. In all these cases the decay exponent is close
to the positive Lyapunov exponent. For hyperbolic conservative systems, the
power-law decay of the distance autocorrelation tends to be guided by the
smallest Lyapunov exponent.Comment: 7 pages, 8 figure
Characterizing Weak Chaos using Time Series of Lyapunov Exponents
We investigate chaos in mixed-phase-space Hamiltonian systems using time
series of the finite- time Lyapunov exponents. The methodology we propose uses
the number of Lyapunov exponents close to zero to define regimes of ordered
(stickiness), semi-ordered (or semi-chaotic), and strongly chaotic motion. The
dynamics is then investigated looking at the consecutive time spent in each
regime, the transition between different regimes, and the regions in the
phase-space associated to them. Applying our methodology to a chain of coupled
standard maps we obtain: (i) that it allows for an improved numerical
characterization of stickiness in high-dimensional Hamiltonian systems, when
compared to the previous analyses based on the distribution of recurrence
times; (ii) that the transition probabilities between different regimes are
determined by the phase-space volume associated to the corresponding regions;
(iii) the dependence of the Lyapunov exponents with the coupling strength.Comment: 8 pages, 6 figure
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