26 research outputs found
The effect of temperature on generic stable periodic structures in the parameter space of dissipative relativistic standard map
In this work, we have characterized changes in the dynamics of a
two-dimensional relativistic standard map in the presence of dissipation and
specially when it is submitted to thermal effects modeled by a Gaussian noise
reservoir. By the addition of thermal noise in the dissipative relativistic
standard map (DRSM) it is possible to suppress typical stable periodic
structures (SPSs) embedded in the chaotic domains of parameter space for large
enough temperature strengths. Smaller SPSs are first affected by thermal
effects, starting from their borders, as a function of temperature. To estimate
the necessary temperature strength capable to destroy those SPSs we use the
largest Lyapunov exponent to obtain the critical temperature () diagrams.
For critical temperatures the chaotic behavior takes place with the suppression
of periodic motion, although, the temperature strengths considered in this work
are not so large to convert the deterministic features of the underlying system
into a stochastic ones.Comment: 8 pages and 7 figures, accepted to publication in EPJ
Instability statistics and mixing rates
We claim that looking at probability distributions of finite time largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of polynomial decay rates of time correlations and Poincar\ue9 recurrences in the-quite-delicate case of dynamical systems with weak chaotic properties
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
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
Instability statistics and mixing rates
We claim that looking at probability distributions of \emph{finite time}
largest Lyapunov exponents, and more precisely studying their large deviation
properties, yields an extremely powerful technique to get quantitative
estimates of polynomial decay rates of time correlations and Poincar\'e
recurrences in the -quite delicate- case of dynamical systems with weak chaotic
properties.Comment: 5 pages, 5 figure
Gauss map and Lyapunov exponents of interacting particles in a billiard
We show that the Lyapunov exponent (LE) of periodic orbits with Lebesgue
measure zero from the Gauss map can be used to determine the main qualitative
behavior of the LE of a Hamiltonian system. The Hamiltonian system is a
one-dimensional box with two particles interacting via a Yukawa potential and
does not possess Kolmogorov-Arnold-Moser (KAM) curves. In our case the Gauss
map is applied to the mass ratio between particles. Besides
the main qualitative behavior, some unexpected peaks in the dependence
of the mean LE and the appearance of 'stickness' in phase space can also be
understand via LE from the Gauss map. This shows a nice example of the relation
between the "instability" of the continued fraction representation of a number
with the stability of non-periodic curves (no KAM curves) from the physical
model. Our results also confirm the intuition that pseudo-integrable systems
with more complicated invariant surfaces of the flow (higher genus) should be
more unstable under perturbation.Comment: 13 pages, 2 figure