2,221 research outputs found
The triangle map: a model of quantum chaos
We study an area preserving parabolic map which emerges from the Poincar\' e
map of a billiard particle inside an elongated triangle. We provide numerical
evidence that the motion is ergodic and mixing. Moreover, when considered on
the cylinder, the motion appear to follow a gaussian diffusive process.Comment: 4 pages in RevTeX with 4 figures (in 6 eps-files
Measurement and Information Extraction in Complex Dynamics Quantum Computation
We address the problem related to the extraction of the information in the
simulation of complex dynamics quantum computation. Here we present an example
where important information can be extracted efficiently by means of quantum
simulations. We show how to extract efficiently the localization length, the
mean square deviation and the system characteristic frequency. We show how this
methods work on a dynamical model, the Sawtooth Map, that is characterized by
very different dynamical regimes: from near integrable to fully developed
chaos; it also exhibits quantum dynamical localization.Comment: 8 pages, 4 figures, Proceeding of "First International Workshop
DICE2002 - Piombino (Tuscany), (2002)
Quantum Ergodicity and Localization in Conservative Systems: the Wigner Band Random Matrix Model
First theoretical and numerical results on the global structure of the energy
shell, the Green function spectra and the eigenfunctions, both localized and
ergodic, in a generic conservative quantum system are presented. In case of
quantum localization the eigenfunctions are shown to be typically narrow and
solid, with centers randomly scattered within the semicircle energy shell while
the Green function spectral density (local spectral density of states) is
extended over the whole shell, but sparse.Comment: 4 pages in RevTex and 4 Postscript figures; presented to Phys. Lett.
Quantum chaos and the double-slit experiment
We report on the numerical simulation of the double-slit experiment, where
the initial wave-packet is bounded inside a billiard domain with perfectly
reflecting walls. If the shape of the billiard is such that the classical ray
dynamics is regular, we obtain interference fringes whose visibility can be
controlled by changing the parameters of the initial state. However, if we
modify the shape of the billiard thus rendering classical (ray) dynamics fully
chaotic, the interference fringes disappear and the intensity on the screen
becomes the (classical) sum of intensities for the two corresponding one-slit
experiments. Thus we show a clear and fundamental example in which transition
to chaotic motion in a deterministic classical system, in absence of any
external noise, leads to a profound modification in the quantum behaviour.Comment: 5 pages, 4 figure
Anomalous diffusion and dynamical localization in a parabolic map
We study numerically classical and quantum dynamics of a piecewise parabolic
area preserving map on a cylinder which emerges from the bounce map of
elongated triangular billiards. The classical map exhibits anomalous diffusion.
Quantization of the same map results in a system with dynamical localization
and pure point spectrum.Comment: 4 pages in RevTeX (4 ps-figures included
The role of quasi-momentum in the resonant dynamics of the atom-optics kicked rotor
We examine the effect of the initial atomic momentum distribution on the
dynamics of the atom-optical realisation of the quantum kicked rotor. The atoms
are kicked by a pulsed optical lattice, the periodicity of which implies that
quasi-momentum is conserved in the transport problem. We study and compare
experimentally and theoretically two resonant limits of the kicked rotor: in
the vicinity of the quantum resonances and in the semiclassical limit of
vanishing kicking period. It is found that for the same experimental
distribution of quasi-momenta, significant deviations from the kicked rotor
model are induced close to quantum resonance, while close to the classical
resonance (i.e. for small kicking period) the effect of the quasi-momentum
vanishes.Comment: 10 pages, 4 figures, to be published in J. Phys. A, Special Issue on
'Trends in Quantum Chaotic Scattering
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.
Quantum Ratchet Accelerator without a Bichromatic Lattice Potential
In a quantum ratchet accelerator system, a linearly increasing directed
current can be dynamically generated without using a biased field. Generic
quantum ratchet acceleration with full classical chaos [Gong and Brumer, Phys.
Rev. Lett. 97, 240602 (2006)] constitutes a new element of quantum chaos and an
interesting violation of a sum rule of classical ratchet transport. Here we
propose a simple quantum ratchet accelerator model that can also generate
linearly increasing quantum current with full classical chaos. This new model
does not require a bichromatic lattice potential. It is based on a variant of
an on-resonance kicked-rotor system, periodically kicked by two optical lattice
potentials of the same lattice constant, but with unequal amplitudes and a
fixed phase shift between them. The dependence of the ratchet current
acceleration rate on the system parameters is studied in detail. The cold-atom
version of our new quantum ratchet accelerator model should be realizable by
introducing slight modifications to current cold-atom experiments.Comment: 9 pages, 6 figures, submitted to Phys. Rev.
Controlled Quantum State Transfer in a Spin Chain
Control of the transfer of quantum information encoded in quantum wavepackets
moving along a spin chain is demonstrated. Specifically, based on a
relationship with control in a paradigm of quantum chaos, it is shown that
wavepackets with slow dispersion can automatically emerge from a class of
initial superposition states involving only a few spins, and that arbitrary
unspecified travelling wavepackets can be nondestructively stopped and later
relaunched with perfection. The results establish an interesting application of
quantum chaos studies in quantum information science.Comment: 6 pages, 3 figures, to appear in Physical Review
Quantum Resonances of Kicked Rotor and SU(q) group
The quantum kicked rotor (QKR) map is embedded into a continuous unitary
transformation generated by a time-independent quasi-Hamiltonian. In some
vicinity of a quantum resonance of order , we relate the problem to the {\it
regular} motion along a circle in a -component inhomogeneous
"magnetic" field of a quantum particle with intrinsic degrees of freedom
described by the group. This motion is in parallel with the classical
phase oscillations near a non-linear resonance.Comment: RevTeX, 4 pages, 3 figure
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