1,448 research outputs found
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
Entanglement between two subsystems, the Wigner semicircle and extreme value statistics
The entanglement between two arbitrary subsystems of random pure states is
studied via properties of the density matrix's partial transpose,
. The density of states of is close to the
semicircle law when both subsystems have dimensions which are not too small and
are of the same order. A simple random matrix model for the partial transpose
is found to capture the entanglement properties well, including a transition
across a critical dimension. Log-negativity is used to quantify entanglement
between subsystems and analytic formulas for this are derived based on the
simple model. The skewness of the eigenvalue density of is
derived analytically, using the average of the third moment over the ensemble
of random pure states. The third moment after partial transpose is also shown
to be related to a generalization of the Kempe invariant. The smallest
eigenvalue after partial transpose is found to follow the extreme value
statistics of random matrices, namely the Tracy-Widom distribution. This
distribution, with relevant parameters obtained from the model, is found to be
useful in calculating the fraction of entangled states at critical dimensions.
These results are tested in a quantum dynamical system of three coupled
standard maps, where one finds that if the parameters represent a strongly
chaotic system, the results are close to those of random states, although there
are some systematic deviations at critical dimensions.Comment: Substantially improved version (now 43 pages, 10 figures) that is
accepted for publication in Phys. Rev.
Quantum Poincare Recurrences for Hydrogen Atom in a Microwave Field
We study the time dependence of the ionization probability of Rydberg atoms
driven by a microwave field, both in classical and in quantum mechanics. The
quantum survival probability follows the classical one up to the Heisenberg
time and then decays algebraically as P(t) ~ 1/t. This decay law derives from
the exponentially long times required to escape from some region of the phase
space, due to tunneling and localization effects. We also provide parameter
values which should allow to observe such decay in laboratory experiments.Comment: revtex, 4 pages, 4 figure
Classical diffusion in double-delta-kicked particles
We investigate the classical chaotic diffusion of atoms subjected to {\em
pairs} of closely spaced pulses (`kicks) from standing waves of light (the
-KP). Recent experimental studies with cold atoms implied an
underlying classical diffusion of type very different from the well-known
paradigm of Hamiltonian chaos, the Standard Map.
The kicks in each pair are separated by a small time interval , which together with the kick strength , characterizes the transport.
Phase space for the -KP is partitioned into momentum `cells' partially
separated by momentum-trapping regions where diffusion is slow. We present here
an analytical derivation of the classical diffusion for a -KP
including all important correlations which were used to analyze the
experimental data.
We find a new asymptotic () regime of `hindered' diffusion:
while for the Standard Map the diffusion rate, for , oscillates about the uncorrelated, rate , we find
analytically, that the -KP can equal, but never diffuses faster than,
a random walk rate.
We argue this is due to the destruction of the important classical
`accelerator modes' of the Standard Map.
We analyze the experimental regime , where
quantum localisation lengths are affected by fractal
cell boundaries. We find an approximate asymptotic diffusion rate , in correspondence to a regime in the Standard Map
associated with 'golden-ratio' cantori.Comment: 14 pages, 10 figures, error in equation in appendix correcte
Observation of high-order quantum resonances in the kicked rotor
Quantum resonances in the kicked rotor are characterized by a dramatically
increased energy absorption rate, in stark contrast to the momentum
localization generally observed. These resonances occur when the scaled
Planck's constant hbar=(r/s)*4pi, for any integers r and s. However only the
hbar=r*2pi resonances are easily observable. We have observed high-order
quantum resonances (s>2) utilizing a sample of low temperature, non-condensed
atoms and a pulsed optical standing wave. Resonances are observed for
hbar=(r/16)*4pi r=2-6. Quantum numerical simulations suggest that our
observation of high-order resonances indicates a larger coherence length than
expected from an initially thermal atomic sample
The Sato Grassmannian and the CH hierarchy
We discuss how the Camassa-Holm hierarchy can be framed within the geometry
of the Sato Grassmannian.Comment: 10 pages, no figure
Universality in quantum chaos and the one parameter scaling theory
We adapt the one parameter scaling theory (OPT) to the context of quantum
chaos. As a result we propose a more precise characterization of the
universality classes associated to Wigner-Dyson and Poisson statistics which
takes into account Anderson localization effects. Based also on the OPT we
predict a new universality class in quantum chaos related to the
metal-insulator transition and provide several examples. In low dimensions it
is characterized by classical superdiffusion or a fractal spectrum, in higher
dimensions it can also have a purely quantum origin as in the case of
disordered systems. Our findings open the possibility of studying the metal
insulator transition experimentally in a much broader type of systems.Comment: 4 pages, 2 figures, acknowledgment added, typos correcte
Accelerator dynamics of a fractional kicked rotor
It is shown that the Weyl fractional derivative can quantize an open system.
A fractional kicked rotor is studied in the framework of the fractional
Schrodinger equation. The system is described by the non-Hermitian Hamiltonian
by virtue of the Weyl fractional derivative. Violation of space symmetry leads
to acceleration of the orbital momentum. Quantum localization saturates this
acceleration, such that the average value of the orbital momentum can be a
direct current and the system behaves like a ratchet. The classical counterpart
is a nonlinear kicked rotor with absorbing boundary conditions.Comment: Submitted for publication in Phys. Rev.
Conservative chaotic map as a model of quantum many-body environment
We study the dynamics of the entanglement between two qubits coupled to a
common chaotic environment, described by the quantum kicked rotator model. We
show that the kicked rotator, which is a single-particle deterministic
dynamical system, can reproduce the effects of a pure dephasing many-body bath.
Indeed, in the semiclassical limit the interaction with the kicked rotator can
be described as a random phase-kick, so that decoherence is induced in the
two-qubit system. We also show that our model can efficiently simulate
non-Markovian environments.Comment: 8 pages, 4 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.
- …