124 research outputs found
Spreading of wave packets in disordered systems with tunable nonlinearity
We study the spreading of single-site excitations in one-dimensional
disordered Klein-Gordon chains with tunable nonlinearity for different values of . We perform extensive numerical
simulations where wave packets are evolved a) without and, b) with dephasing in
normal mode space. Subdiffusive spreading is observed with the second moment of
wave packets growing as . The dependence of the numerically
computed exponent on is in very good agreement with our
theoretical predictions both for the evolution of the wave packet with and
without dephasing (for in the latter case). We discuss evidence
of the existence of a regime of strong chaos, and observe destruction of
Anderson localization in the packet tails for small values of .Comment: 9 pages, 7 figure
Chaoticity without thermalisation in disordered lattices
We study chaoticity and thermalization in Bose-Einstein condensates in
disordered lattices, described by the discrete nonlinear Schr\"odinger equation
(DNLS). A symplectic integration method allows us to accurately obtain both the
full phase space trajectories and their maximum Lyapunov exponents (mLEs),
which characterize their chaoticity. We find that disorder destroys ergodicity
by breaking up phase space into subsystems that are effectively disjoint on
experimentally relevant timescales, even though energetically, classical
localisation cannot occur. This leads us to conclude that the mLE is a very
poor ergodicity indicator, since it is not sensitive to the trajectory being
confined to a subregion of phase space. The eventual thermalization of a BEC in
a disordered lattice cannot be predicted based only on the chaoticity of its
phase space trajectory
Polydispersed Granular Chains: From Long-lived Chaotic Anderson-like Localization to Energy Equipartition
We investigate the dynamics of highly polydispersed finite granular chains.
From the spatio-spectral properties of small vibrations, we identify which
particular single-particle displacements lead to energy localization. Then, we
address a fundamental question: Do granular nonlinearities lead to chaotic
dynamics and if so, does chaos destroy this energy localization? Our numerical
simulations show that for moderate nonlinearities, although the overall system
behaves chaotically, it can exhibit long lasting energy localization for
particular single particle excitations. On the other hand, for sufficiently
strong nonlinearities, connected with contact breaking, the granular chain
reaches energy equipartition and an equilibrium chaotic state, independent of
the initial position excitation
Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices
We numerically investigate the characteristics of chaos evolution during wave
packet spreading in two typical one-dimensional nonlinear disordered lattices:
the Klein-Gordon system and the discrete nonlinear Schr\"{o}dinger equation
model. Completing previous investigations \cite{SGF13} we verify that chaotic
dynamics is slowing down both for the so-called `weak' and `strong chaos'
dynamical regimes encountered in these systems, without showing any signs of a
crossover to regular dynamics. The value of the finite-time maximum Lyapunov
exponent decays in time as , with being different from the
value observed in cases of regular motion. In particular,
(weak chaos) and
(strong chaos) for both models, indicating the dynamical differences of the two
regimes and the generality of the underlying chaotic mechanisms. The
spatiotemporal evolution of the deviation vector associated with
reveals the meandering of chaotic seeds inside the wave packet, which is needed
for obtaining the chaotization of the lattice's excited part.Comment: 11 pages, 10 figure
How does the Smaller Alignment Index (SALI) distinguish order from chaos?
The ability of the Smaller Alignment Index (SALI) to distinguish chaotic from
ordered motion, has been demonstrated recently in several
publications.\cite{Sk01,GRACM} Basically it is observed that in chaotic regions
the SALI goes to zero very rapidly, while it fluctuates around a nonzero value
in ordered regions. In this paper, we make a first step forward explaining
these results by studying in detail the evolution of small deviations from
regular orbits lying on the invariant tori of an {\bf integrable} 2D
Hamiltonian system. We show that, in general, any two initial deviation vectors
will eventually fall on the ``tangent space'' of the torus, pointing in
different directions due to the different dynamics of the 2 integrals of
motion, which means that the SALI (or the smaller angle between these vectors)
will oscillate away from zero for all time.Comment: To appear in Progress of Theoretical Physics Supplemen
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