1,270 research outputs found
Regular and Anomalous Quantum Diffusion in the Fibonacci Kicked Rotator
We study the dynamics of a quantum rotator kicked according to the
almost-periodic Fibonacci sequence. A special numerical technique allows us to
carry on this investigation for as many as kicks. It is shown that
above a critical kick strength the excitation of the system is well described
by regular diffusion, while below this border it becomes anomalous, and
sub-diffusive. A law for the dependence of the exponent of anomalous
sub-diffusion on the system parameters is established numerically. The analogy
between these results and quantum diffusion in models of quasi-crystal and in
the kicked Harper system is discussed.Comment: 7 pages, 4 figures, submitted to Phys. Rev.
On conformally recurrent manifolds of dimension greater than 4
Conformally recurrent pseudo-Riemannian manifolds of dimension n>4 are
investigated. The Weyl tensor is represented as a Kulkarni-Nomizu product. If
the square of the Weyl tensor is nonzero, a covariantly constant symmetric
tensor is constructed, that is quadratic in the Weyl tensor. Then, by Grycak's
theorem, the explicit expression of the traceless part of the Ricci tensor is
obtained, up to a scalar function. The Ricci tensor has at most two distinct
eigenvalues, and the recurrence vector is an eigenvector. Lorentzian
conformally recurrent manifolds are then considered. If the square of the Weyl
tensor is nonzero, the manifold is decomposable. A null recurrence vector makes
the Weyl tensor of algebraic type IId or higher in the Bel - Debever - Ortaggio
classification, while a time-like recurrence vector makes the Weyl tensor
purely electric.Comment: Title changed and typos corrected. 14 page
Quantum entropies and decoherence for the multiparticle quantum Arnol’d Cat â€
I study the scaling behavior in the physical parameters of dynamical entropies, classical and quantum, in a specifically devised model of collision-induced decoherence in a chaotic system. The treatment is fully canonical and no approximations are involved or infinite limits taken. I present this model in a detailed way, in order to clarify my views in the debate about the nature, definition, and relevance of quantum chaos
Cyclotron-Bloch dynamics of a quantum particle in a two-dimensional lattice II
We study the quantum dynamics of a charged particle in a two-dimensional
lattice, subject to constant and homogeneous electric and magnetic fields. We
find that different regimes characterize these motions, depending on a
combination of conditions, corresponding to weak and strong electric field
intensities, rational or irrational directions of the electric field with
respect to the lattice, and small or large values of the magnetic (Peierls)
phase.Comment: 22 pages, 11 figure
Coarse-Grained Probabilistic Automata Mimicking Chaotic Systems
Discretization of phase space usually nullifies chaos in dynamical systems.
We show that if randomness is associated with discretization dynamical chaos
may survive and be indistinguishable from that of the original chaotic system,
when an entropic, coarse-grained analysis is performed. Relevance of this
phenomenon to the problem of quantum chaos is discussed.Comment: 4 pages, 4 figure
Cyclotron-Bloch dynamics of a quantum particle in a 2D lattice
This paper studies the quantum dynamics of a charged particle in a 2D square
lattice, under the influence of electric and magnetic fields, the former being
aligned with one of the lattice axes and the latter perpendicular to the
lattice plane. While in free space these dynamics consist of uniform motions in
the direction orthogonal to the electric field vector, we find that, in a
lattice, this directed drift takes place only for specific initial conditions
and for electric field magnitudes smaller than a critical value. Otherwise, the
quantum wave--packet spreads ballistically in both directions orthogonal to the
electric field. We quantify this ballistic spreading and identify the subspace
of initial conditions insuring directed transport with the drift velocity. We
also describe the effect of disorder in the system.Comment: APS preprint format, 23 pages, 11 figure
Electron Wave Filters from Inverse Scattering Theory
Semiconductor heterostructures with prescribed energy dependence of the
transmittance can be designed by combining: {\em a)} Pad\'e approximant
reconstruction of the S-matrix; {\em b)} inverse scattering theory for
Schro\"dinger's equation; {\em c)} a unitary transformation which takes into
account the variable mass effects. The resultant continuous concentration
profile can be digitized into an easily realizable rectangular-wells structure.
For illustration, we give the specifications of a 2 narrow band-pass 12 layer
filter with the high energy peak more than {\em twice
narrower} than the other.Comment: 4 pages, Revtex with one eps figur
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