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

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 $U$ 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 $U$ and fine spectral structure for small $U$.Comment: revtex, 4 pages, 5 figure