1,898 research outputs found
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
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
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
Dynamically localized systems: entanglement exponential sensitivity and efficient quantum simulations
We study the pairwise entanglement present in a quantum computer that
simulates a dynamically localized system. We show that the concurrence is
exponentially sensitive to changes in the Hamiltonian of the simulated system.
Moreover, concurrence is exponentially sensitive to the ``logic'' position of
the qubits chosen. These sensitivities could be experimentally checked
efficiently by means of quantum simulations with less than ten qubits. We also
show that the feasibility of efficient quantum simulations is deeply connected
to the dynamical regime of the simulated system.Comment: 5 pages, 6 figure
Quantum localization and cantori in chaotic billiards
We study the quantum behaviour of the stadium billiard. We discuss how the
interplay between quantum localization and the rich structure of the classical
phase space influences the quantum dynamics. The analysis of this model leads
to new insight in the understanding of quantum properties of classically
chaotic systems.Comment: 4 pages in RevTex with 4 eps figures include
Quantum Fractal Fluctuations
We numerically analyse quantum survival probability fluctuations in an open,
classically chaotic system. In a quasi-classical regime, and in the presence of
classical mixed phase space, such fluctuations are believed to exhibit a
fractal pattern, on the grounds of semiclassical arguments. In contrast, we
work in a classical regime of complete chaoticity, and in a deep quantum regime
of strong localization. We provide evidence that fluctuations are still
fractal, due to the slow, purely quantum algebraic decay in time produced by
dynamical localization. Such findings considerably enlarge the scope of the
existing theory.Comment: revtex, 4 pages, 5 figure
Fourier's Law in a Quantum Spin Chain and the Onset of Quantum Chaos
We study heat transport in a nonequilibrium steady state of a quantum
interacting spin chain. We provide clear numerical evidence of the validity of
Fourier law. The regime of normal conductivity is shown to set in at the
transition to quantum chaos.Comment: 4 pages, 5 figures, RevTe
Dynamical Localization: Hydrogen Atoms in Magnetic and Microwave fields
We show that dynamical localization for excited hydrogen atoms in magnetic
and microwave fields takes place at quite low microwave frequency much lower
than the Kepler frequency. The estimates of localization length are given for
different parameter regimes, showing that the quantum delocalization border
drops significantly as compared to the case of zero magnetic field. This opens
up broad possibilities for laboratory investigations.Comment: revtex, 11 pages, 3 figures, to appear in Phys. Rev. A, Feb (1997
Directed deterministic classical transport: symmetry breaking and beyond
We consider transport properties of a double delta-kicked system, in a regime
where all the symmetries (spatial and temporal) that could prevent directed
transport are removed. We analytically investigate the (non trivial) behavior
of the classical current and diffusion properties and show that the results are
in good agreement with numerical computations. The role of dissipation for a
meaningful classical ratchet behavior is also discussed.Comment: 10 pages, 20 figure
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