1,099 research outputs found
Fractal Spectrum of a Quasi_periodically Driven Spin System
We numerically perform a spectral analysis of a quasi-periodically driven
spin 1/2 system, the spectrum of which is Singular Continuous. We compute
fractal dimensions of spectral measures and discuss their connections with the
time behaviour of various dynamical quantities, such as the moments of the
distribution of the wave packet. Our data suggest a close similarity between
the information dimension of the spectrum and the exponent ruling the algebraic
growth of the 'entropic width' of wavepackets.Comment: 17 pages, RevTex, 5 figs. available on request from
[email protected]
On the Spectrum of the Resonant Quantum Kicked Rotor
It is proven that none of the bands in the quasi-energy spectrum of the
Quantum Kicked Rotor is flat at any primitive resonance of any order.
Perturbative estimates of bandwidths at small kick strength are established for
the case of primitive resonances of prime order. Different bands scale with
different powers of the kick strength, due to degeneracies in the spectrum of
the free rotor.Comment: Description of related published work has been expanded in the
Introductio
Chaos from turbulence: stochastic-chaotic equilibrium in turbulent convection at high Rayleigh numbers
It is shown that correlation function of the mean wind velocity generated by
a turbulent thermal convection (Rayleigh number ) exhibits
exponential decay with a very long correlation time, while corresponding
largest Lyapunov exponent is certainly positive. These results together with
the reconstructed phase portrait indicate presence of chaotic component in the
examined mean wind. Telegraph approximation is also used to study relative
contribution of the chaotic and stochastic components to the mean wind
fluctuations and an equilibrium between these components has been studied in
detail
Regimes of stability of accelerator modes
The phase diagram of a simple area-preserving map, which was motivated by the
quantum dynamics of cold atoms, is explored analytically and numerically.
Periodic orbits of a given winding ratio are found to exist within wedge-shaped
regions in the phase diagrams, which are analogous to the Arnol'd tongues which
have been extensively studied for a variety of dynamical systems, mostly
dissipative ones. A rich variety of bifurcations of various types are observed,
as well as period doubling cascades. Stability of periodic orbits is analyzed
in detail.Comment: Submitted to Physica
Pseudo-classical theory for fidelity of nearly resonant quantum rotors
Using a semiclassical ansatz we analytically predict for the fidelity of
delta-kicked rotors the occurrence of revivals and the disappearance of
intermediate revival peaks arising from the breaking of a symmetry in the
initial conditions. A numerical verification of the predicted effects is given
and experimental ramifications are discussed.Comment: Shortened and improved versio
What determines the spreading of a wave packet?
The multifractal dimensions D2^mu and D2^psi of the energy spectrum and
eigenfunctions, resp., are shown to determine the asymptotic scaling of the
width of a spreading wave packet. For systems where the shape of the wave
packet is preserved the k-th moment increases as t^(k*beta) with
beta=D2^mu/D2^psi, while in general t^(k*beta) is an optimal lower bound.
Furthermore, we show that in d dimensions asymptotically in time the center of
any wave packet decreases spatially as a power law with exponent D_2^psi - d
and present numerical support for these results.Comment: Physical Review Letters to appear, 4 pages postscript with figure
Upper bounds on wavepacket spreading for random Jacobi matrices
A method is presented for proving upper bounds on the moments of the position
operator when the dynamics of quantum wavepackets is governed by a random
(possibly correlated) Jacobi matrix. As an application, one obtains sharp upper
bounds on the diffusion exponents for random polymer models, coinciding with
the lower bounds obtained in a prior work. The second application is an
elementary argument (not using multiscale analysis or the Aizenman-Molchanov
method) showing that under the condition of uniformly positive Lyapunov
exponents, the moments of the position operator grow at most logarithmically in
time.Comment: final version, to appear in CM
Quantum Accelerator Modes near Higher-Order Resonances
Quantum Accelerator Modes have been experimentally observed, and
theoretically explained, in the dynamics of kicked cold atoms in the presence
of gravity, when the kicking period is close to a half-integer multiple of the
Talbot time. We generalize the theory to the case when the kicking period is
sufficiently close to any rational multiple of the Talbot time, and thus
predict new rich families of experimentally observable Quantum Accelerator
Modes.Comment: Inaccurate reference [12] has been amende
Decay of Quantum Accelerator Modes
Experimentally observable Quantum Accelerator Modes are used as a test case
for the study of some general aspects of quantum decay from classical stable
islands immersed in a chaotic sea. The modes are shown to correspond to
metastable states, analogous to the Wannier-Stark resonances. Different regimes
of tunneling, marked by different quantitative dependence of the lifetimes on
1/hbar, are identified, depending on the resolution of KAM substructures that
is achieved on the scale of hbar. The theory of Resonance Assisted Tunneling
introduced by Brodier, Schlagheck, and Ullmo [9], is revisited, and found to
well describe decay whenever applicable.Comment: 16 pages, 11 encapsulated postscript figures (figures with a better
resolution are available upon request to the authors); added reference for
section
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