Correlated Markov Quantum Walks

We consider the discrete time unitary dynamics given by a quantum walk on $\Z^d$ performed by a particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes place, followed by a shift on the lattice, conditioned on the coin state of the particle. We study the large time behavior of the quantum mechanical probability distribution of the position observable in $\Z^d$ for random updates of the coin states of the following form. The random sequences of unitary updates are given by a site dependent function of a Markov chain in time, with the following properties: on each site, they share the same stationnary Markovian distribution and, for each fixed time, they form a deterministic periodic pattern on the lattice. We prove a Feynman-Kac formula to express the characteristic function of the averaged distribution over the randomness at time $n$ in terms of the nth power of an operator $M$. By analyzing the spectrum of $M$, we show that this distribution posesses a drift proportional to the time and its centered counterpart displays a diffusive behavior with a diffusion matrix we compute. Moderate and large deviations principles are also proven to hold for the averaged distribution and the limit of the suitably rescaled corresponding characteristic function is shown to satisfy a diffusion equation. An example of random updates for which the analysis of the distribution can be performed without averaging is worked out. The random distribution displays a deterministic drift proportional to time and its centered counterpart gives rise to a random diffusion matrix whose law we compute. We complete the picture by presenting an uncorrelated example.Comment: 37 pages. arXiv admin note: substantial text overlap with arXiv:1010.400

Segregation and precipitation of Er in Ge

Although Er-doped Genanomaterials are attractive for photonic applications, very little is known about the basic properties of Er in Ge. Here, the authors study the annealing behavior of Geimplanted with keV Er ions to doses resulting in ≲1at.% of Er. Large redistribution of Er, with segregation at the amorphous/crystalline interface, starts at ≳500°C, while lower temperatures are required for material recrystallization. However, even at 400°C, Er forms precipitates. The concentration of Er trapped in the bulk after recrystallization decreases with increasing temperature but is independent of the initial bulk Er concentration for the range of ion doses studied here.Work at the ANU was supported by the ARC

Nature of the supercritical mesophase

It has been reported that at temperatures above the critical there is no “continuity of liquid and gas”, as originally hypothesized by van der Waals [1]. Rather, both gas and liquid phases, with characteristic properties as such, extend to supercritical temperatures [2]-[4]. Each phase is bounded by the locus of a percolation transition, i.e. a higher-order thermodynamic phase change associated with percolation of gas clusters in a large void, or liquid interstitial vacancies in a large cluster. Between these two-phase bounds, it is reported there exists a mesophase that resembles an otherwise homogeneous dispersion of gas micro-bubbles in liquid (foam) and a dispersion of liquid micro-droplets in gas (mist). Such a colloidal-like state of a pure one-component fluid represents a hitherto unchartered equilibrium state of matter besides pure solid, liquid or gas. Here we provide compelling evidence, from molecular dynamics (MD) simulations, for the existence of this supercritical mesophase and its colloidal nature. We report preliminary results of computer simulations for a model fluid using a simplistic representation of atoms or molecules, i.e. a hard-core repulsion with an attraction so short that the atoms are referred to as “adhesive spheres”. Molecular clusters, and hence percolation transitions, are unambiguously defined. Graphics of color-coded clusters show colloidal characteristics of the supercritical mesophase. We append this Letter to Natural Science with a debate on the scientific merits of its content courtesy of correspondence with Nature (Appendix)info:eu-repo/semantics/publishedVersio

Space-time variation of ciliates related to environmental factors in 15 nearshore stations of the Gulf of Gabes

Diversity and structure of ciliate communities in the Gulf of Gabes (Tunisia) were investigated based on a survey of 15 nearshore stations along 237 Km, by monthly sampling over a 1-year. Ciliated protozoa were identified to genus and/or species level and enumerated. Statistic tools were used to explain the ciliates assemblage. High ciliates species richness from 133 taxa was recorded, including new records of 76 species. This study showed a longitudinal distribution of ciliate communities, which are organized in northern stations (from Tabia to Harbor of Gabes) and southern stations (from Zarrat to Jabiat Haj Ali). The number of taxa increased significantly in northern stations but decreased in the southern. This distribution was mainly influenced by the salinity and phytoplankton abundance. Ciliate taxa were grouped into fives size-classes: 15-30 µm, 30-50 µm, 50-100 µm, 100-200 µm and >200 µm. In terms of abundance, most abundant size groups were small ciliates (15-30 μm) accounted from 15 to 79 %, while the greatest biomass contribution came from the 50-100 μm size classes. We thus conclude high diversity of ciliates communities that showed a geographical distribution influenced by abiotic and biotic factors along the coast of Gulf of Gabes

Evolution of Superconductivity in Electron-Doped Cuprates: Magneto-Raman Spectroscopy

The electron-doped cuprates Pr_{2-x}Ce_xCuO_4 and Nd_{2-x}Ce_xCuO_4 have been studied by electronic Raman spectroscopy across the entire region of the superconducting (SC) phase diagram. The SC pairing strength is found to be consistent with a weak-coupling regime except in the under-doped region where we observe an in-gap collective mode at 4.5 k_{B}T_c while the maximum amplitude of the SC gap is ~8 k_{B}T_{c}. In the normal state, doped carriers divide into coherent quasi-particles (QPs) and carriers that remain incoherent. The coherent QPs mainly reside in the vicinity of (\pi/2, \pi/2) regions of the Brillouin zone (BZ). We find that only coherent QPs contribute to the superfluid density in the B_{2g} channel. The persistence of SC coherence peaks in the B_{2g} channel for all dopings implies that superconductivity is mainly governed by interactions between the hole-like coherent QPs in the vicinity of (\pi/2, \pi/2) regions of the BZ. We establish that superconductivity in the electron-doped cuprates occurs primarily due to pairing and condensation of hole-like carriers. We have also studied the excitations across the SC gap by Raman spectroscopy as a function of temperature (T) and magnetic field (H) for several different cerium dopings (x). Effective upper critical field lines H*_{c2}(T, x) at which the superfluid stiffness vanishes and H^{2\Delta}_{c2}(T, x) at which the SC gap amplitude is suppressed by field have been determined; H^{2\Delta}_{c2}(T, x) is larger than H*_{c2}(T, x) for all doping concentrations. The difference between the two quantities suggests the presence of phase fluctuations that increase for x< 0.15. It is found that the magnetic field suppresses the magnitude of the SC gap linearly at surprisingly small fields.Comment: 13 pages, 8 figures; submitted to Phys. Rev.

Limit theorems and ergodicity for general bootstrap random walks

Given the increments of a simple symmetric random walk $(X_n)_{n\ge0}$, we characterize all possible ways of recycling these increments into a simple symmetric random walk $(Y_n)_{n\ge0}$ adapted to the filtration of $(X_n)_{n\ge0}$. We study the long term behavior of a suitably normalized two-dimensional process $((X_n,Y_n))_{n\ge0}$. In particular, we provide necessary and sufficient conditions for the process to converge to a two-dimensional Brownian motion (possibly degenerate). We also discuss cases in which the limit is not Gaussian. Finally, we provide a simple necessary and sufficient condition for the ergodicity of the recycling transformation, thus generalizing results from Dubins and Smorodinsky (1992) and Fujita (2008), and solving the discrete version of the open problem of the ergodicity of the general L\'evy transformation (see Mansuy and Yor, 2006).Comment: 22 pages, 2 figure

Bacteriological Quality of Fresh Vegetables and Peeled Sugar-Cane Obtained from Selected Markets in Zaria, Nigeria

Fresh vegetables and peeled sugar-cane serves as an essential component of a healthy diet, but despite their benefit they are prompt to bacterial contamination. The bacteriological quality of four types of fresh vegetables and peeled sugar-cane obtained from selected markets in Zaria, Nigeria was determined using standard microbiological method. The fresh vegetables, peeled sugar-cane, water and hand-swab samples were collected from four different locations namely; Samaru, Sabon-gari, Tudun-wada and Zaria-city. The total bacteria plate counts ranged from 3.3 x 106 cfu/g to 1.6 x 107 cfu/g with Tudu-wada having the highest bacteria load in lettuce. The coliform count of fresh vegetables and peeled sugar-cane varies from 1.3 x 104 to 8.6 x 105 cfu/g in the entire markets with Tudu-wada having the highest value in cucumber, the counts were obviously above specified Standard of 105 cfu/g and  103 cfu/g (ICMSF, 1978). Pathogenic bacteria isolated include; Citrobacter fruendii, Escherichia coli, Enterobacter spp., Klebsiella. spp., Shigella spp., Serratia spp., Cronobacter sakazaki, Staphylococcus aureus, Pseudomonas spp., and others Staphylococci spp.. This study showed that, fresh vegetables and peeled sugar-cane are contaminated with pathogenic bacteria making them unsafe for human consumption; hence fresh produce should be pre- treated thoroughly, so as to reduce the risk of food- borne outbreaks. Keywords: Pathogenic bacteria · Bacteriological quality, Microbiological method, Coliform counts and food- borne outbreaks. DOI: 10.7176/JNSR/12-8-02 Publication date: April 30th 202

Local and regional factors influencing zooplankton communities in the connected Kasseb Reservoir, Tunisia

Associations between zooplankton community structure and abiotic (temperature, dissolved oxygen, turbidity, nutriments) and biotic factors (chlorophyll a and phytoplankton community) were examined, in Kasseb Reservoir, northern Tunisia. Samples were taken bimonthly from July to December 2002 at 3 sampling stations (deepest station: Station 1, Brik River: Station 2 and M’Zaz Stama River: Station 3). From our results it is evident that zooplankton exhibit seasonally and spatially heterogeneous distribution. The highest density of zooplankton was recorded in September at a depth of 5 m (10.8 × 103 ind·l-1). At Station 1 cyclopoid copepods (65% of total abundance) were the most abundant group followed by Cladocera (21% of total abundance). At Station 2 (93% of total abundance) and Station 3 (98% of total abundance) cyclopoid copepodswere numerically dominant throughout the study period. Canonical correspondence analysis (CCA) was used to estimate the influence of abiotic and biotic factors in structuring the zooplankton assemblage. Zooplankton abundance was negatively correlated with turbidity (r= -0.381,