arXiv subjects

Laura Rebuzzini

Publications and source records attributed to Laura Rebuzzini.

10 recordsLinked to original sources

arXiv2010

Higher order statistics in the annulus square billiard: transport and polyspectra

Classical transport in a doubly connected polygonal billiard, i.e. the annulus square billiard, is considered. Dynamical properties of the billiard flow with a fixed initial direction are analyzed by means of the moments of arbitrary order of the number of revolutions around the inner square, accumulated by the particles during the evolution. An "anomalous" diffusion is found: the moment of order q exhibits an algebraic growth in time with an exponent different from q/2, like in the normal case. Transport features are related to spectral properties of the system, which are reconstructed by Fourier transforming time correlation functions. An analytic estimate for the growth exponent of integer order moments is derived as a function of the scaling index at zero frequency of the spectral measure, associated to the angle spanned by the particles. The n-th order moment is expressed in terms of a multiple-time correlation function, depending on n-1 time intervals, which is shown to be linked to higher order density spectra (polyspectra), by a generalization of the Wiener-Khincin Theorem. Analytic results are confirmed by numerical simulations.

nlin.CD↗

arXiv2008

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.

quant-ph↗

arXiv2007

Effects of atomic interactions on Quantum Accelerator Modes

We consider the influence of the inclusion of interatomic interactions on the delta-kicked accelerator model. Our analysis concerns in particular quantum accelerator modes, namely quantum ballistic transport near quantal resonances. The atomic interaction is modelled by a Gross-Pitaevskii cubic nonlinearity, and we address both attractive (focusing) and repulsive (defocusing) cases. The most remarkable effect is enhancement or damping of the accelerator modes, depending on the sign of the nonlinear parameter. We provide arguments showing that the effect persists beyond mean-field description, and lies within the experimentally accessible parameter range.

nlin.CD↗

arXiv2006

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.

quant-ph↗

arXiv2005

Arnol'd Tongues and Quantum Accelerator Modes

The stable periodic orbits of an area-preserving map on the 2-torus, which is formally a variant of the Standard Map, have been shown to explain the quantum accelerator modes that were discovered in experiments with laser-cooled atoms. We show that their parametric dependence exhibits Arnol'd-like tongues and perform a perturbative analysis of such structures. We thus explain the arithmetical organisation of the accelerator modes and discuss experimental implications thereof.

quant-ph↗

arXiv2005

Delocalized and Resonant Quantum Transport in Nonlinear Generalizations of the Kicked Rotor Model

We analyze the effects of a nonlinear cubic perturbation on the delta-Kicked Rotor. We consider two different models, in which the nonlinear term acts either in the position or in the momentum representation. We numerically investigate the modifications induced by the nonlinearity in the quantum transport in both localized and resonant regimes and a comparison between the results for the two models is presented. Analyzing the momentum distributions and the increase of the mean square momentum, we find that the quantum resonances asymptotically are very stable with respect to the nonlinear perturbation of the rotor's phase evolution. For an intermittent time regime, the nonlinearity even enhances the resonant quantum transport, leading to superballistic motion.

nlin.CD↗

arXiv2003

Effects of a nonlinear perturbation on dynamical tunneling in cold atoms

We perform a numerical analysis of the effects of a nonlinear perturbation on the quantum dynamics of two models describing non-interacting cold atoms in a standing wave of light with a periodical modulated amplitude $A(t)$. One model is the driven pendulum, considered in ref.\cite{raiz1}, and the other is a variant of the well-known Kicked Rotator Model. In absence of the nonlinear perturbation, the system is invariant under some discrete symmetries and quantum dynamical tunnelling between symmetric classical islands is found. The presence of nonlinearity destroys tunnelling, breaking the symmetries of the system. Finally, further consequences of nonlinearity in the kicked rotator case are considered.

nlin.CD↗

arXiv2002

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.

nlin.CD↗

arXiv2002

Nonlinearity effects in the kicked oscillator

The quantum kicked oscillator is known to display a remarkable richness of dynamical behaviour, from ballistic spreading to dynamical localization. Here we investigate the effects of a Gross Pitaevskii nonlinearity on quantum motion, and provide evidence that the qualitative features depend strongly on the parameters of the system.

nlin.CD↗

arXiv2002

A Theory for Quantum Accelerator Modes in Atom Optics

Unexpected accelerator modes were recently observed experimentally for cold cesium atoms when driven in the presence of gravity. A detailed theoretical explanation of this quantum effect is presented here. The theory makes use of invariance properties of the system, that are similar to the ones of solids, leading to a separation into independent kicked rotor problems. The analytical solution makes use of a limit that is very similar to the semiclassical limit, but with a small parameter that is not Planck's constant, but rather the detuning from the frequency that is resonant in absence of gravity.

nlin.CD↗