1,971 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.
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
Statistical properties of eigenvalues for an operating quantum computer with static imperfections
We investigate the transition to quantum chaos, induced by static
imperfections, for an operating quantum computer that simulates efficiently a
dynamical quantum system, the sawtooth map. For the different dynamical regimes
of the map, we discuss the quantum chaos border induced by static imperfections
by analyzing the statistical properties of the quantum computer eigenvalues.
For small imperfection strengths the level spacing statistics is close to the
case of quasi-integrable systems while above the border it is described by the
random matrix theory. We have found that the border drops exponentially with
the number of qubits, both in the ergodic and quasi-integrable dynamical
regimes of the map characterized by a complex phase space structure. On the
contrary, the regime with integrable map dynamics remains more stable against
static imperfections since in this case the border drops only algebraically
with the number of qubits.Comment: 9 pages, 10 figure
Quantum Resonances and Regularity Islands in Quantum Maps
We study analytically as well as numerically the dynamics of a quantum map
near a quantum resonance of an order q. The map is embedded into a continuous
unitary transformation generated by a time-independent quasi-Hamiltonian. Such
a Hamiltonian generates at the very point of the resonance a local gauge
transformation described the unitary unimodular group SU(q). The resonant
energy growth of is attributed to the zero Liouville eigenmodes of the
generator in the adjoint representation of the group while the non-zero modes
yield saturating with time contribution. In a vicinity of a given resonance,
the quasi-Hamiltonian is then found in the form of power expansion with respect
to the detuning from the resonance. The problem is related in this way to the
motion along a circle in a (q^2-1)-component inhomogeneous "magnetic" field of
a quantum particle with intrinsic degrees of freedom described by the SU(q)
group. This motion is in parallel with the classical phase oscillations near a
non-linear resonance. The most important role is played by the resonances with
the orders much smaller than the typical localization length, q << l. Such
resonances master for exponentially long though finite times the motion in some
domains around them. Explicit analytical solution is possible for a few lowest
and strongest resonances.Comment: 28 pages (LaTeX), 11 ps figures, submitted to PR
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
Parametric Evolution for a Deformed Cavity
We consider a classically chaotic system that is described by a Hamiltonian
H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x
controls a deformation of the boundary. The quantum-eigenstates of the system
are |n(x)>. We describe how the parametric kernel P(n|m) = , also
known as the local density of states, evolves as a function of x-x0. We
illuminate the non-unitary nature of this parametric evolution, the emergence
of non-perturbative features, the final non-universal saturation, and the
limitations of random-wave considerations. The parametric evolution is
demonstrated numerically for two distinct representative deformation processes.Comment: 13 pages, 8 figures, improved introduction, to be published in Phys.
Rev.
Comment on "Coherent Ratchets in Driven Bose-Einstein Condensates"
C. E. Creffield and F. Sols (Phys. Rev. Lett. 103, 200601 (2009)) recently
reported finite, directed time-averaged ratchet current, for a noninteracting
quantum particle in a periodic potential even when time-reversal symmetry
holds. As we explain in this Comment, this result is incorrect, that is,
time-reversal symmetry implies a vanishing current.Comment: revised versio
Heat conduction in one dimensional systems: Fourier law, chaos, and heat control
In this paper we give a brief review of the relation between microscopic
dynamical properties and the Fourier law of heat conduction as well as the
connection between anomalous conduction and anomalous diffusion. We then
discuss the possibility to control the heat flow.Comment: 15 pages, 11 figures. To be published in the Proceedings of the NATO
Advanced Research Workshop on Nonlinear Dynamics and Fundamental
Interactions, Tashkent, Uzbekistan, Octo. 11-16, 200
Phase-space reconstruction of an atomic chaotic system
We consider the dynamics of a single atom submitted to periodic pulses of a
far-detuned standing wave generated by a high-finesse optical cavity, which is
an atomic version of the well-known ``kicked rotor''. We show that the
classical phase-space map can be ``reconstructed'' by monitoring the
transmission of the cavity. We also studied the effect of spontaneous emission
on the reconstruction, and put limits to the maximum acceptable spontaneous
emission rate.Comment: 5 figures, submitted to PR
- …