Statistical properties of the localization measure in a finite-dimensional model of the quantum kicked rotator

We study the quantum kicked rotator in the classically fully chaotic regime $K=10$ and for various values of the quantum parameter $k$ using Izrailev's $N$-dimensional model for various $N \le 3000$, which in the limit $N \rightarrow \infty$ tends to the exact quantized kicked rotator. By numerically calculating the eigenfunctions in the basis of the angular momentum we find that the localization length ${\cal L}$ for fixed parameter values has a certain distribution, in fact its inverse is Gaussian distributed, in analogy and in connection with the distribution of finite time Lyapunov exponents of Hamilton systems. However, unlike the case of the finite time Lyapunov exponents, this distribution is found to be independent of $N$, and thus survives the limit $N=\infty$. This is different from the tight-binding model of Anderson localization. The reason is that the finite bandwidth approximation of the underlying Hamilton dynamical system in the Shepelyansky picture (D.L. Shepelyansky, {\em Phys. Rev. Lett.} {\bf 56}, 677 (1986)) does not apply rigorously. This observation explains the strong fluctuations in the scaling laws of the kicked rotator, such as e.g. the entropy localization measure as a function of the scaling parameter $\Lambda={\cal L}/N$, where $\cal L$ is the theoretical value of the localization length in the semiclassical approximation. These results call for a more refined theory of the localization length in the quantum kicked rotator and in similar Floquet systems, where we must predict not only the mean value of the inverse of the localization length $\cal L$ but also its (Gaussian) distribution, in particular the variance. In order to complete our studies we numerically analyze the related behavior of finite time Lyapunov exponents in the standard map and of the 2$\times$2 transfer matrix formalism. This paper is extending our recent work.Comment: 12 pages, 9 figures (accepted for publication in Physical Review E). arXiv admin note: text overlap with arXiv:1301.418

Police Liability for False Arrest or Imprisonment

It is difficult to arrive at a valid distinction between false arrest and false imprisonment. The two causes of action are practically indistinguishable. When there is a false arrest there is a false imprisonment, but in a false arrest detention is based on asserted legal authority to enforce the processes of the law. A false imprisonment can arise between private persons for a private end with no relevance to the administration of criminal law. Our primary concern here, of course, is solely with a detention under color of law. This article purports to describe the various situations in which an officer of the law can expose himself to liability for false imprisonment

Probing the local dynamics of periodic orbits by the generalized alignment index (GALI) method

As originally formulated, the Generalized Alignment Index (GALI) method of chaos detection has so far been applied to distinguish quasiperiodic from chaotic motion in conservative nonlinear dynamical systems. In this paper we extend its realm of applicability by using it to investigate the local dynamics of periodic orbits. We show theoretically and verify numerically that for stable periodic orbits the GALIs tend to zero following particular power laws for Hamiltonian flows, while they fluctuate around non-zero values for symplectic maps. By comparison, the GALIs of unstable periodic orbits tend exponentially to zero, both for flows and maps. We also apply the GALIs for investigating the dynamics in the neighborhood of periodic orbits, and show that for chaotic solutions influenced by the homoclinic tangle of unstable periodic orbits, the GALIs can exhibit a remarkable oscillatory behavior during which their amplitudes change by many orders of magnitude. Finally, we use the GALI method to elucidate further the connection between the dynamics of Hamiltonian flows and symplectic maps. In particular, we show that, using for the computation of GALIs the components of deviation vectors orthogonal to the direction of motion, the indices of stable periodic orbits behave for flows as they do for maps.Comment: 17 pages, 9 figures (accepted for publication in Int. J. of Bifurcation and Chaos

Surface Modification of Polyimide Films for Inkjet-Printing of Flexible Electronic Devices

Kapton polyimide films are one of the most commonly used flexible and robust substrates for flexible electronic devices due to their excellent thermal, chemical, mechanical, and electrical properties. However, such films feature an inert and highly hydrophobic surface that inhibits the deposition of functional materials with water-based fluids (solutions, suspensions, inkjet inks, etc.), which raise the need for their surface modification to reduce their inherent surface inertness and/or hydrophobicity in order to allow for the fabrication of electronic devices on the substrates. Traditional Kapton surface modification approaches use harsh conditions that not only cause environmental and safety problems but also compromise the structural integrity and the properties of the substrates. This chapter focuses on two recently-developed mild and environmentally friendly wet chemical approaches for surface modification of Kapton HN films. Unlike the traditional methods that target the polyimide matrix of Kapton films, these two methods target the slip additive embedded in the polyimide matrix. The surface modified Kapton films resulted from these two methods allowed for not only great printability of both water- and organic solvent-based inks (thus facilitating the full-inkjet-printing of entire flexible electronic devices) but also strong adhesion between the inkjet-printed traces and the substrate films

Conformal Magnetic Composite RFID for Wearable RF and Bio-Monitoring Applications

©2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.10.1109/TMTT.2008.2006810This paper introduces for the first time a novel flexible magnetic composite material for RF identification (RFID) and wearable RF antennas. First, one conformal RFID tag working at 480 MHz is designed and fabricated as a benchmarking prototype and the miniaturization concept is verified. Then, the impact of the material is thoroughly investigated using a hybrid method involving electromagnetic and statistical tools. Two separate statistical experiments are performed, one for the analysis of the impact of the relative permittivity and permeability of the proposed material and the other for the evaluation of the impact of the dielectric and magnetic loss on the antenna performance. Finally, the effect of the bending of the antenna is investigated, both on the S-parameters and on the radiation pattern. The successful implementation of the flexible magnetic composite material enables the significant miniaturization of RF passives and antennas in UHF frequency bands, especially when conformal modules that can be easily fine-tuned are required in critical biomedical and pharmaceutical applications

Interplay Between Chaotic and Regular Motion in a Time-Dependent Barred Galaxy Model

We study the distinction and quantification of chaotic and regular motion in a time-dependent Hamiltonian barred galaxy model. Recently, a strong correlation was found between the strength of the bar and the presence of chaotic motion in this system, as models with relatively strong bars were shown to exhibit stronger chaotic behavior compared to those having a weaker bar component. Here, we attempt to further explore this connection by studying the interplay between chaotic and regular behavior of star orbits when the parameters of the model evolve in time. This happens for example when one introduces linear time dependence in the mass parameters of the model to mimic, in some general sense, the effect of self-consistent interactions of the actual N-body problem. We thus observe, in this simple time-dependent model also, that the increase of the bar's mass leads to an increase of the system's chaoticity. We propose a new way of using the Generalized Alignment Index (GALI) method as a reliable criterion to estimate the relative fraction of chaotic vs. regular orbits in such time-dependent potentials, which proves to be much more efficient than the computation of Lyapunov exponents. In particular, GALI is able to capture subtle changes in the nature of an orbit (or ensemble of orbits) even for relatively small time intervals, which makes it ideal for detecting dynamical transitions in time-dependent systems.Comment: 21 pages, 9 figures (minor typos fixed) to appear in J. Phys. A: Math. Theo