661 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
Quasi-stationary chaotic states in multi-dimensional Hamiltonian systems
We study numerically statistical distributions of sums of chaotic orbit
coordinates, viewed as independent random variables, in weakly chaotic regimes
of three multi-dimensional Hamiltonian systems: Two Fermi-Pasta-Ulam
(FPU-) oscillator chains with different boundary conditions and numbers
of particles and a microplasma of identical ions confined in a Penning trap and
repelled by mutual Coulomb interactions. For the FPU systems we show that, when
chaos is limited within "small size" phase space regions, statistical
distributions of sums of chaotic variables are well approximated for
surprisingly long times (typically up to ) by a -Gaussian
() distribution and tend to a Gaussian () for longer times, as the
orbits eventually enter into "large size" chaotic domains. However, in
agreement with other studies, we find in certain cases that the -Gaussian is
not the only possible distribution that can fit the data, as our sums may be
better approximated by a different so-called "crossover" function attributed to
finite-size effects. In the case of the microplasma Hamiltonian, we make use of
these -Gaussian distributions to identify two energy regimes of "weak
chaos"-one where the system melts and one where it transforms from liquid to a
gas state-by observing where the -index of the distribution increases
significantly above the value of strong chaos.Comment: 32 pages, 13 figures, Submitted for publication to Physica
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
Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi--Pasta--Ulam lattices by the Generalized Alignment Index method
The recently introduced GALI method is used for rapidly detecting chaos,
determining the dimensionality of regular motion and predicting slow diffusion
in multi--dimensional Hamiltonian systems. We propose an efficient computation
of the GALI indices, which represent volume elements of randomly chosen
deviation vectors from a given orbit, based on the Singular Value Decomposition
(SVD) algorithm. We obtain theoretically and verify numerically asymptotic
estimates of GALIs long--time behavior in the case of regular orbits lying on
low--dimensional tori. The GALI indices are applied to rapidly detect
chaotic oscillations, identify low--dimensional tori of Fermi--Pasta--Ulam
(FPU) lattices at low energies and predict weak diffusion away from
quasiperiodic motion, long before it is actually observed in the oscillations.Comment: 10 pages, 5 figures, submitted for publication in European Physical
Journal - Special Topics. Revised version: Small explanatory additions to the
text and addition of some references. A small figure chang
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