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

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

Decay of Quantum Accelerator Modes

Experimentally observable Quantum Accelerator Modes are used as a test case for the study of some general aspects of quantum decay from classical stable islands immersed in a chaotic sea. The modes are shown to correspond to metastable states, analogous to the Wannier-Stark resonances. Different regimes of tunneling, marked by different quantitative dependence of the lifetimes on 1/hbar, are identified, depending on the resolution of KAM substructures that is achieved on the scale of hbar. The theory of Resonance Assisted Tunneling introduced by Brodier, Schlagheck, and Ullmo [9], is revisited, and found to well describe decay whenever applicable.Comment: 16 pages, 11 encapsulated postscript figures (figures with a better resolution are available upon request to the authors); added reference for section