Localization for Random Unitary Operators

We consider unitary analogs of $1-$dimensional Anderson models on $l^2(\Z)$ defined by the product $U_\omega=D_\omega S$ where $S$ is a deterministic unitary and $D_\omega$ is a diagonal matrix of i.i.d. random phases. The operator $S$ is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We prove that the spectrum of $U_\omega$ is pure point almost surely for all values of the parameter of $S$. We provide similar results for unitary operators defined on $l^2(\N)$ together with an application to orthogonal polynomials on the unit circle. We get almost sure localization for polynomials characterized by Verblunski coefficients of constant modulus and correlated random phases

Temporal Interferometry: A Mechanism for Controlling Qubit Transitions During Twisted Rapid Passage with Possible Application to Quantum Computing

In an adiabatic rapid passage experiment, the Bloch vector of a two-level system (qubit) is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle $\phi (t)$ at the same time that it is inverted. For polynomial twist: $\phi (t) \sim Bt^{n}$. We show that for $n \geq 3$, multiple avoided crossings can occur during the inversion of the external field, and that these crossings give rise to strong interference effects in the qubit transition probability. The transition probability is found to be a function of the twist strength $B$, which can be used to control the time-separation of the avoided crossings, and hence the character of the interference. Constructive and destructive interference are possible. The interference effects are a consequence of the temporal phase coherence of the wavefunction. The ability to vary this coherence by varying the temporal separation of the avoided crossings renders twisted rapid passage with adjustable twist strength into a temporal interferometer through which qubit transitions can be greatly enhanced or suppressed. Possible application of this interference mechanism to construction of fast fault-tolerant quantum CNOT and NOT gates is discussed.Comment: 29 pages, 16 figures, submitted to Phys. Rev.

Pulse-driven quantum dynamics beyond the impulsive regime

We review various unitary time-dependent perturbation theories and compare them formally and numerically. We show that the Kolmogorov-Arnold-Moser technique performs better owing to both the superexponential character of correction terms and the possibility to optimize the accuracy of a given level of approximation which is explored in details here. As an illustration, we consider a two-level system driven by short pulses beyond the sudden limit.Comment: 15 pages, 5 color figure

Frequency Dependence of Quantum Localization in a Periodically Driven System

We study the quantum localization phenomena for a random matrix model belonging to the Gaussian orthogonal ensemble (GOE). An oscillating external field is applied on the system. After the transient time evolution, energy is saturated to various values depending on the frequencies. We investigate the frequency dependence of the saturated energy. This dependence cannot be explained by a naive picture of successive independent Landau-Zener transitions at avoided level crossing points. The effect of quantum interference is essential. We define the number of Floquet states which have large overlap with the initial state, and calculate its frequency dependence. The number of Floquet states shows approximately linear dependence on the frequency, when the frequency is small. Comparing the localization length in Floquet states and that in energy states from the viewpoint of the Anderson localization, we conclude that the Landau-Zener picture works for the local transition processes between levels.Comment: 12 pages and 6 figure

The Chandra ACIS Survey of M33 (ChASeM33): The final source catalog

This study presents the final source catalog of the Chandra ACIS Survey of M33 (ChASeM33). With a total exposure time of 1.4 Ms, ChASeM33 covers ~70% of the D25 isophote (R\approx4kpc) of M33 and provides the deepest, most complete, and detailed look at a spiral galaxy in X-rays. The source catalog includes 662 sources, reaches a limiting unabsorbed luminosity of ~2.4x10^(34) erg/s in the 0.35-8.0keV energy band, and contains source positions, source net counts, fluxes and significances in several energy bands, and information on source variability. The analysis challenges posed by ChASeM33 and the techniques adopted to address these challenges are discussed. To constrain the nature of the detected X-ray source, hardness ratios were constructed and spectra were fit for 254 sources, followup MMT spectra of 116 sources were acquired, and cross-correlations with previous X-ray catalogs and other multi-wavelength data were generated. Based on this effort, 183 of the 662 ChASeM33 sources could be identified. Finally, the luminosity function for the detected point sources as well as the one for the X-ray binaries in M33 is presented. The luminosity functions in the soft band (0.5-2.0 keV) and the hard band (2.0-8.0 keV) have a limiting luminosity at the 90% completeness limit of 4.0x10^(34) erg/s and 1.6x10^(35) erg/s (for D=817kpc), respectively, which is significantly lower than what was reported by previous X-ray binary population studies in galaxies more distant than M33. The resulting distribution is consistent with a dominant population of high mass X-ray binaries as would be expected for M33.Comment: 186 pages, 11 figures, 10 tables. Accepted for publication in the ApJS. For a high resolution version of the paper, see http://hea-www.harvard.edu/vlp_m33_public

The rise and fall of methanotrophy following a deepwater oil-well blowout

The blowout of the Macondo oil well in the Gulf of Mexico in April 2010 injected up to 500,000 tonnes of natural gas, mainly methane, into the deep sea1. Most of the methane released was thought to have been consumed by marine microbes between July and August 20102, 3. Here, we report spatially extensive measurements of methane concentrations and oxidation rates in the nine months following the spill. We show that although gas-rich deepwater plumes were a short-lived feature, water column concentrations of methane remained above background levels throughout the rest of the year. Rates of microbial methane oxidation peaked in the deepwater plumes in May and early June, coincident with a rapid rise in the abundance of known and new methane-oxidizing microbes. At this time, rates of methane oxidation reached up to 5,900 nmol l−1 d−1—the highest rates documented in the global pelagic ocean before the blowout4. Rates of methane oxidation fell to less than 50 nmol l−1 d−1 in late June, and continued to decline throughout the remainder of the year. We suggest the precipitous drop in methane consumption in late June, despite the persistence of methane in the water column, underscores the important role that physiological and environmental factors play in constraining the activity of methane-oxidizing bacteria in the Gulf of Mexico

Influence of supramolecular forces on the linear viscoelasticity of gluten

Stress relaxation behavior of hydrated gluten networks was investigated by means of rheometry combined with μ-computed tomography (μ-CT) imaging. Stress relaxation behavior was followed over a wide temperature range (0–70 °C). Modulation of intermolecular bonds was achieved with urea or ascorbic acid in an effort to elucidate the presiding intermolecular interactions over gluten network relaxation. Master curves of viscoelasticity were constructed, and relaxation spectra were computed revealing three relaxation regimes for all samples. Relaxation commences with a well-defined short-time regime where Rouse-like modes dominate, followed by a power law region displaying continuous relaxation concluding in a terminal zone. In the latter zone, poroelastic relaxation due to water migration in the nanoporous structure of the network also contributes to the stress relief in the material. Hydrogen bonding between adjacent protein chains was identified as the determinant force that influences the relaxation of the networks. Changes in intermolecular interactions also resulted in changes in microstructure of the material that was also linked to the relaxation behavior of the networks

Statistical Characterization of the Chandra Source Catalog

The first release of the Chandra Source Catalog (CSC) contains ~95,000 X-ray sources in a total area of ~0.75% of the entire sky, using data from ~3,900 separate ACIS observations of a multitude of different types of X-ray sources. In order to maximize the scientific benefit of such a large, heterogeneous data-set, careful characterization of the statistical properties of the catalog, i.e., completeness, sensitivity, false source rate, and accuracy of source properties, is required. Characterization efforts of other, large Chandra catalogs, such as the ChaMP Point Source Catalog (Kim et al. 2007) or the 2 Mega-second Deep Field Surveys (Alexander et al. 2003), while informative, cannot serve this purpose, since the CSC analysis procedures are significantly different and the range of allowable data is much less restrictive. We describe here the characterization process for the CSC. This process includes both a comparison of real CSC results with those of other, deeper Chandra catalogs of the same targets and extensive simulations of blank-sky and point source populations.Comment: To be published in the Astrophysical Journal Supplement Series (Fig. 52 replaced with a version which astro-ph can convert to PDF without issues.

Co-ordination of local policies for urban development and public transportation in four Swiss cities

The present article aims at assessing the possibility for urban areas to coordinate local policies of urban development and public transportation and at explaining the differences in this achievement between urban regions. In order to do so, the study draws support from two empirical sources: a historical analysis of the "mass-production" generated by the public service sectors in the field of transport and urban development in the cities of Basel, Bern, Geneva, and Lausanne since 1950, and a series of six case studies in these four cities. The study identifies factors located both at context level regarding morphological and geographical conditions as well as institutional settings and case-specific idiosyncrasies regarding organizational structure, past policy decisions, as well as vocational cultures that determine the possibility for urban areas to meet the need for policy coordination