1,059 research outputs found
A classical scaling theory of quantum resonances
The quantum resonances occurring with delta-kicked particles are studied with
the help of a fictitious classical limit, establishing a direct correspondence
between the nearly resonant quantum motion and the classical resonances of a
related system. A scaling law which characterizes the structure of the resonant
peaks is derived and numerically demonstrated.Comment: 4 pages, 2 Fig
Pseudo-classical theory for fidelity of nearly resonant quantum rotors
Using a semiclassical ansatz we analytically predict for the fidelity of
delta-kicked rotors the occurrence of revivals and the disappearance of
intermediate revival peaks arising from the breaking of a symmetry in the
initial conditions. A numerical verification of the predicted effects is given
and experimental ramifications are discussed.Comment: Shortened and improved versio
Stable Quantum Resonances in Atom Optics
A theory for stabilization of quantum resonances by a mechanism similar to
one leading to classical resonances in nonlinear systems is presented. It
explains recent surprising experimental results, obtained for cold Cesium atoms
when driven in the presence of gravity, and leads to further predictions. The
theory makes use of invariance properties of the system, that are similar to
those of solids, allowing for separation into independent kicked rotor
problems. The analysis relies on a fictitious classical limit where the small
parameter is {\em not} Planck's constant, but rather the detuning from the
frequency that is resonant in absence of gravity.Comment: 5 pages, 3 figure
What determines the spreading of a wave packet?
The multifractal dimensions D2^mu and D2^psi of the energy spectrum and
eigenfunctions, resp., are shown to determine the asymptotic scaling of the
width of a spreading wave packet. For systems where the shape of the wave
packet is preserved the k-th moment increases as t^(k*beta) with
beta=D2^mu/D2^psi, while in general t^(k*beta) is an optimal lower bound.
Furthermore, we show that in d dimensions asymptotically in time the center of
any wave packet decreases spatially as a power law with exponent D_2^psi - d
and present numerical support for these results.Comment: Physical Review Letters to appear, 4 pages postscript with figure
Quantum Accelerator Modes near Higher-Order Resonances
Quantum Accelerator Modes have been experimentally observed, and
theoretically explained, in the dynamics of kicked cold atoms in the presence
of gravity, when the kicking period is close to a half-integer multiple of the
Talbot time. We generalize the theory to the case when the kicking period is
sufficiently close to any rational multiple of the Talbot time, and thus
predict new rich families of experimentally observable Quantum Accelerator
Modes.Comment: Inaccurate reference [12] has been amende
Quantum Return Probability for Substitution Potentials
We propose an effective exponent ruling the algebraic decay of the average
quantum return probability for discrete Schrodinger operators. We compute it
for some non-periodic substitution potentials with different degrees of
randomness, and do not find a complete qualitative agreement with the spectral
type of the substitution sequences themselves, i.e., more random the sequence
smaller such exponent.Comment: Latex, 13 pages, 6 figures; to be published in Journal of Physics
Optimizing aesthetic outcomes after goldilocks mastectomy: A new method of nipple reconstruction
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
Double butterfly spectrum for two interacting particles in the Harper model
We study the effect of interparticle interaction on the spectrum of the
Harper model and show that it leads to a pure-point component arising from the
multifractal spectrum of non interacting problem. Our numerical studies allow
to understand the global structure of the spectrum. Analytical approach
developed permits to understand the origin of localized states in the limit of
strong interaction and fine spectral structure for small .Comment: revtex, 4 pages, 5 figure
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