6,919 research outputs found

    Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

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    We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states. Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled ``spins'' which are elements of u(1,1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams.Comment: 39 pages, 1 figur

    Charge Distribution Near Oxygen Vacancies in Reduced Ceria

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    Understanding the electronic charge distribution around oxygen vacancies in transition metal and rare earth oxides is a scientific challenge of considerable technological importance. We show how significant information about the charge distribution around vacancies in cerium oxide can be gained from a study of high resolution crystal structures of higher order oxides which exhibit ordering of oxygen vacancies. Specifically, we consider the implications of a bond valence sum analysis of Ce7_{7}O12_{12} and Ce11_{11}O20_{20}. To illuminate our analysis we show alternative representations of the crystal structures in terms of orderly arrays of co-ordination defects and in terms of flourite-type modules. We found that in Ce7_{7}O12_{12}, the excess charge resulting from removal of an oxygen atom delocalizes among all three triclinic Ce sites closest to the O vacancy. In Ce11_{11}O20_{20}, the charge localizes on the next nearest neighbour Ce atoms. Our main result is that the charge prefers to distribute itself so that it is farthest away from the O vacancies. This contradicts \emph{the standard picture of charge localisation} which assumes that each of the two excess electrons localises on one of the cerium ions nearest to the vacancy. This standard picture is assumed in most calculations based on density functional theory (DFT). Based on the known crystal structure of Pr6_{6}O11_{11}, we also predict that the charge in Ce6_{6}O11_{11} will be found in the second coordination shell of the O vacancy. Although this review focuses on bulk cerium oxides our approach to characterising electronic properties of oxygen vacancies and the physical insights gained should also be relevant to surface defects and to other rare earth and transition metal oxides.Comment: 20 pages, 23 figures. The replacement file has a new format for the figures are the document layout but no change in content. v3 has the following main changes: 1. The abstract and introduction were extensively revised. 2. Sec. IV was removed. 3. The Conclusion was rewritte

    Transport properties of the metallic state of overdoped cuprate superconductors from an anisotropic marginal Fermi liquid model

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    We consider the implications of a phenomenological model self-energy for the charge transport properties of the metallic phase of the overdoped cuprate superconductors. The self-energy is the sum of two terms with characteristic dependencies on temperature, frequency, location on the Fermi surface, and doping. The first term is isotropic over the Fermi surface, independent of doping, and has the frequency and temperature dependence characteristic of a Fermi liquid. The second term is anisotropic over the Fermi surface (vanishing at the same points as the superconducting energy gap), strongly varies with doping (scaling roughly with TcT_c, the superconducting transition temperature), and has the frequency and temperature dependence characteristic of a marginal Fermi liquid. Previously it has been shown this self-energy can describe a range of experimental data including angle-dependent magnetoresistance (ADMR) and quasi-particle renormalisations determined from specific heat, quantum oscillations, and angle-resolved photo-emission spectroscopy (ARPES). Without introducing new parameters and neglecting vertex corrections we show that this model self-energy can give a quantitative description of the temperature and doping dependence of a range of reported transport properties of Tl2201 samples. These include the intra-layer resistivity, the frequency dependent optical conductivity, the intra-layer magnetoresistance, and the Hall coefficient. The temperature dependence of the latter two are particularly sensitive to the anisotropy of the scattering rate and to the shape of the Fermi surface. In contrast, the temperature dependence of the Hall angle is dominated by the Fermi liquid contribution to the self-energy that determines the scattering rate in the nodal regions of the Fermi surface.Comment: 17 pages, 16 figure

    How linear features alter predator movement and the functional\ud response

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    In areas of oil and gas exploration, seismic lines have been reported to alter the movement patterns of wolves (Canis lupus). We developed a mechanistic first passage time model, based on an anisotropic elliptic partial differential equation, and used this to explore how wolf movement responses to seismic lines influence the encounter rate of the wolves with their prey. The model was parametrized using 5 min GPS location data. These data showed that wolves travelled faster on seismic lines and had a higher probability of staying on a seismic line once they were on it. We simulated wolf movement on a range of seismic line densities and drew implications for the rate of predator–prey interactions as described by the functional response. The functional response exhibited a more than linear increase with respect to prey density (type III) as well as interactions with seismic line density. Encounter rates were significantly higher in landscapes with high seismic line density and were most pronounced at low prey densities. This suggests that prey at low population densities are at higher risk in environments with a high seismic line density unless they learn to avoid them

    The Late Time Light Curve of SN 1998bw Associated with GRB980425

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    We report 139 photometric observations through the B, V, and I filters of the supernova SN 1998bw, an object which is associated with the Gamma-Ray Burst GRB 980425. Detailed light curves of this unique supernova can be compared to theoretical models, so we report here our light curve for 123 days between 27 June 1998 and 28 October 1998. The light curve of SN 1988bw is consistent with those of the Type Ic class. We find that the magnitude-versus-time relation for this supernova is linear to within 0.05 mags in all colors over the entire duration of our study. Our measured uniform decline rates are 0.0141±0.00020.0141 \pm 0.0002, 0.0184±0.00030.0184 \pm 0.0003, and 0.0181±0.00030.0181 \pm 0.0003 magnitudes per day in the B, V, and I bands. The linear decline and the rate of that decline suggest that late time light curve is powered by the radioactive decay of cobalt with some leakage of the gamma rays.Comment: 15 pages, 1 figure, 1 table, Accepted for publication in PAS

    Development of visual size constancy during the 1st year of human infancy.

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    Photothermal Fluctuations as a Fundamental Limit to Low-Frequency Squeezing in a Degenerate Optical Parametric Amplifier

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    We study the effect of photothermal fluctuations on squeezed states of light through the photo-refractive effect and thermal expansion in a degenerate optical parametric amplifier (OPA). We also discuss the effect of the photothermal noise in various cases and how to minimize its undesirable consequences. We find that the photothermal noise in the OPA introduces a significant amount of noise on phase squeezed beams, making them less than ideal for low frequency applications such as gravitational wave (GW) interferometers, whereas amplitude squeezed beams are relatively immune to the photothermal noise and may represent the best choice for application in GW interferometers
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