1,497 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]
Distribution of resonance widths in localized tight-binding models
We numerically analyze the distribution of scattering resonance widths in
one- and quasi-one dimensional tight binding models, in the localized regime.
We detect and discuss an algebraic decay of the distribution, similar, though
not identical, to recent theoretical predictions.Comment: 18 pages, 6 eps figures, to be published in `The European Physical
Journal B
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
A classical scaling theory of quantum resonances
The quantum resonances occurring with delta-kicked particles are studied with
the help of a fictitious classical limit, establishing a direct correspondence
between the nearly resonant quantum motion and the classical resonances of a
related system. A scaling law which characterizes the structure of the resonant
peaks is derived and numerically demonstrated.Comment: 4 pages, 2 Fig
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
Quantum Return Probability for Substitution Potentials
We propose an effective exponent ruling the algebraic decay of the average
quantum return probability for discrete Schrodinger operators. We compute it
for some non-periodic substitution potentials with different degrees of
randomness, and do not find a complete qualitative agreement with the spectral
type of the substitution sequences themselves, i.e., more random the sequence
smaller such exponent.Comment: Latex, 13 pages, 6 figures; to be published in Journal of Physics
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