11,772 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
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
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 CeO and
CeO. 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
CeO, the excess charge resulting from removal of an oxygen atom
delocalizes among all three triclinic Ce sites closest to the O vacancy. In
CeO, 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 PrO, we also
predict that the charge in CeO 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
The performance of arm locking in LISA
For the laser interferometer space antenna (LISA) to reach it's design
sensitivity, the coupling of the free running laser frequency noise to the
signal readout must be reduced by more than 14 orders of magnitude. One
technique employed to reduce the laser frequency noise will be arm locking,
where the laser frequency is locked to the LISA arm length. This paper details
an implementation of arm locking, studies orbital effects, the impact of errors
in the Doppler knowledge, and noise limits. The noise performance of arm
locking is calculated with the inclusion of the dominant expected noise
sources: ultra stable oscillator (clock) noise, spacecraft motion, and shot
noise. Studying these issues reveals that although dual arm locking [A. Sutton
& D. A Shaddock, Phys. Rev. D 78, 082001 (2008).] has advantages over single
(or common) arm locking in terms of allowing high gain, it has disadvantages in
both laser frequency pulling and noise performance. We address this by
proposing a hybrid sensor, retaining the benefits of common and dual arm
locking sensors. We present a detailed design of an arm locking controller and
perform an analysis of the expected performance when used with and without
laser pre-stabilization. We observe that the sensor phase changes beneficially
near unity-gain frequencies of the arm-locking controller, allowing a factor of
10 more gain than previously believed, without degrading stability. We show
that the LISA frequency noise goal can be realized with arm locking and
Time-Delay Interferometry only, without any form of pre-stabilization.Comment: 28 pages, 36 figure
Transport properties of the metallic state of overdoped cuprate superconductors from an anisotropic marginal Fermi liquid model
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 , 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
The Late Time Light Curve of SN 1998bw Associated with GRB980425
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 , , and 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
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