Statistical properties of power-law random banded unitary matrices in the delocalization-localization transition regime

Power-law random banded unitary matrices (PRBUM), whose matrix elements decay in a power-law fashion, were recently proposed to model the critical statistics of the Floquet eigenstates of periodically driven quantum systems. In this work, we numerically study in detail the statistical properties of PRBUM ensembles in the delocalization-localization transition regime. In particular, implications of the delocalization-localization transition for the fractal dimension of the eigenvectors, for the distribution function of the eigenvector components, and for the nearest neighbor spacing statistics of the eigenphases are examined. On the one hand, our results further indicate that a PRBUM ensemble can serve as a unitary analog of the power-law random Hermitian matrix model for Anderson transition. On the other hand, some statistical features unseen before are found from PRBUM. For example, the dependence of the fractal dimension of the eigenvectors of PRBUM upon one ensemble parameter displays features that are quite different from that for the power-law random Hermitian matrix model. Furthermore, in the time-reversal symmetric case the nearest neighbor spacing distribution of PRBUM eigenphases is found to obey a semi-Poisson distribution for a broad range, but display an anomalous level repulsion in the absence of time-reversal symmetry.Comment: 10 pages + 13 fig

Nonlinear level crossing models

We examine the effect of nonlinearity at a level crossing on the probability for nonadiabatic transitions $P$. By using the Dykhne-Davis-Pechukas formula, we derive simple analytic estimates for $P$ for two types of nonlinear crossings. In the first type, the nonlinearity in the detuning appears as a {\it perturbative} correction to the dominant linear time dependence. Then appreciable deviations from the Landau-Zener probability $P_{LZ}$ are found to appear for large couplings only, when $P$ is very small; this explains why the Landau-Zener model is often seen to provide more accurate results than expected. In the second type of nonlinearity, called {\it essential} nonlinearity, the detuning is proportional to an odd power of time. Then the nonadiabatic probability $P$ is qualitatively and quantitatively different from $P_{LZ}$ because on the one hand, it vanishes in an oscillatory manner as the coupling increases, and on the other, it is much larger than $P_{LZ}$. We suggest an experimental situation when this deviation can be observed.Comment: 9 pages final postscript file, two-column revtex style, 5 figure

Chaos assisted tunnelling with cold atoms

In the context of quantum chaos, both theory and numerical analysis predict large fluctuations of the tunnelling transition probabilities when irregular dynamics is present at the classical level. We consider here the non-dissipative quantum evolution of cold atoms trapped in a time-dependent modulated periodic potential generated by two laser beams. We give some precise guidelines for the observation of chaos assisted tunnelling between invariant phase space structures paired by time-reversal symmetry.Comment: submitted to Phys. Rev. E ; 16 pages, 13 figures; figures of better quality can be found at http://www.phys.univ-tours.fr/~mouchet

Location of crossings in the Floquet spectrum of a driven two-level system

Calculation of the Floquet quasi-energies of a system driven by a time-periodic field is an efficient way to understand its dynamics. In particular, the phenomenon of dynamical localization can be related to the presence of close approaches between quasi-energies (either crossings or avoided crossings). We consider here a driven two-level system, and study how the locations of crossings in the quasi-energy spectrum alter as the field parameters are changed. A perturbational scheme provides a direct connection between the form of the driving field and the quasi-energies which is exact in the limit of high frequencies. We firstly obtain relations for the quasi-energies for some common types of applied field in the high-frequency limit. We then show how the locations of the crossings drift as the frequency is reduced, and find a simple empirical formula which describes this drift extremely well in general, and appears to be exact for the specific case of square-wave driving.Comment: 6 pages, 6 figures. Minor changes to text, this version to be published in Physical Review

Atom Optics Quantum Pendulum

We explain the dynamics of cold atoms, initially trapped and cooled in a magneto-optic trap, in a monochromatic stationary standing electromagnetic wave field. In the large detuning limit the system is modeled as a nonlinear quantum pendulum. We show that wave packet evolution of the quantum particle probes parametric regimes in the quantum pendulum which support classical period, quantum mechanical revival and super revival phenomena. Interestingly, complete reconstruction in particular parametric regime at quantum revival times is independent of potential height.Comment: 14 pages, 7 figure

Chromium removal from aqueous solution by a PEI-silica nanocomposite

It is essential and important to determine the adsorption mechanism as well as removal efficiency when using an adsorption technique to remove toxic heavy metals from wastewater. In this research, the removal efficiency and mechanism of chromium removal by a silica-based nanoparticle were investigated. A PEI-silica nanoparticle was synthesized by a one-pot technique and exhibited uniformly well-dispersed PEI polymers in silica particles. The adsorption capacity of chromium ions was determined by a batch adsorption test, with the PEI-silica nanoparticle having a value of 183.7 mg/g and monolayer sorption. Adsorption of chromium ions was affected by the solution pH and altered the nanoparticle surface chemically. First principles calculations of the adsorption energies for the relevant adsorption configurations and XPS peaks of Cr and N showed that Cr(VI), [HCrO4](-) is reduced to two species, Cr(III), CrOH2+ and Cr3+, by an amine group and that Cr(III) and Cr(VI) ions are adsorbed on different functional groups, oxidized N and NH3+

Habitat fragmentation effects on annual survival of the federally protected eastern indigo snake

The eastern indigo snake (Drymarchon couperi) is a federally listed species, most recently threatened by habitat loss and habitat degradation. In an effort to estimate snake survival, a total of 103 individuals (59 males, 44 females) were followed using radio-tracking from January 1998 to March 2004 in three landscape types that had increasing levels of habitat fragmentation: (1) conservation cores; (2) conservation areas along highways; (3) suburbs. Because of a large number of radio-tracking locations underground for which the state of snakes (i.e. alive or dead) could not be assessed, we employed a multistate approach to model snake apparent survival and encounter probability of live and dead snakes. We predicted that male snakes in suburbs would have the lowest annual survival. We found a transmitter implantation effect on snake encounter probability, as snakes implanted on a given occasion had a lower encounter probability on the next visit compared with snakes not implanted on the previous occasion. Our results indicated that adult eastern indigo snakes have relatively high survival in conservation core areas, but greatly reduced survival in conservation areas along highways and in suburbs. These findings indicate that habitat fragmentation is likely to be the critical factor for species’ persistence

Canaveral National Seashore Water Quality and Aquatic Resource Inventory

Mosquito Lagoon is a shallow, bar-built estuary located on the east central Florida Coast, primarily within the KSC boundary. The lagoon and watershed cover approximately 327 sq km (79422 acres) .The Lagoon occupies 159 sq km (37853 acres). Water depths average approximately 1m. The lagoon volume is approximately 1.6 x 10(exp 8)cu m. Water quality in Mosquito Lagoon is good. Salinity data typically range between 20 ppt and 35 ppt. The lowest value recorded was 4.5 ppt and the highest value was 37 ppt. Water temperatures fluctuate 2 - 3 C over a 24 h period. Cold front passage can rapidly alter water temperatures by 5 - 10 C or more in a short period of time. The highest temperature was 33.4 C and the lowest temperature was 8.8 C after a winter storm. Dissolved oxygen concentrations ranged from a low of 0.4 mg/l to a high of 15.3 mg/l. Extended periods of measurements below the Florida Department of Environmental Protection criteria of 4.0 mg/l were observed in fall and spring months suggesting high system respiration and oxygen demand. Metals such as antimony, arsenic, molybdenum and mercury were report as below detection limits for all samples. Cadmium, copper, chromium, silver, and zinc were found to be periodically above the Florida Department of Environmental Protection criteria for Class II and Class III surface waters