6,495 research outputs found
A class of exactly solvable models for the Schrodinger equation
We present a class of confining potentials which allow one to reduce the
one-dimensional Schroodinger equation to a named equation of mathematical
physics, namely either Bessel's or Whittaker's differential equation. In all
cases, we provide closed form expressions for both the symmetric and
antisymmetric wavefunction solutions, each along with an associated
transcendental equation for allowed eigenvalues. The class of potentials
considered contains an example of both cusp-like single wells and a
double-well.Comment: 5 pages, 7 figure
Localization of massless Dirac particles via spatial modulations of the Fermi velocity
The electrons found in Dirac materials are notorious for being difficult to
manipulate due to the Klein phenomenon and absence of backscattering. Here we
investigate how spatial modulations of the Fermi velocity in two-dimensional
Dirac materials can give rise to localization effects, with either full
(zero-dimensional) confinement or partial (one-dimensional) confinement
possible depending on the geometry of the velocity modulation. We present
several exactly solvable models illustrating the nature of the bound states
which arise, revealing how the gradient of the Fermi velocity is crucial for
determining fundamental properties of the bound states such as the zero-point
energy. We discuss the implications for guiding electronic waves in few-mode
waveguides formed by Fermi velocity modulation.Comment: 9 pages, 6 figure
Charged Particle Radiation Damage in Semiconductors, I- Experimental Proton Irradiation of Solar Cells
Proton irradiation of solar cell
One-dimensional Coulomb problem in Dirac materials
We investigate the one-dimensional Coulomb potential with application to a
class of quasirelativistic systems, so-called Dirac-Weyl materials, described
by matrix Hamiltonians. We obtain the exact solution of the shifted and
truncated Coulomb problems, with the wavefunctions expressed in terms of
special functions (namely Whittaker functions), whilst the energy spectrum must
be determined via solutions to transcendental equations. Most notably, there
are critical bandgaps below which certain low-lying quantum states are missing
in a manifestation of atomic collapse.Comment: 7 pages, 5 figure
Bielectron vortices in two-dimensional Dirac semimetals
Searching for new states of matter and unusual quasiparticles in emerging
materials and especially low-dimensional systems is one of the major trends in
contemporary condensed matter physics. Dirac materials, which host
quasiparticles which are described by ultrarelativistic Dirac-like equations,
are of a significant current interest from both a fundamental and applied
physics perspective. Here we show that a pair of two-dimensional massless
Dirac-Weyl fermions can form a bound state independently of the sign of the
inter-particle interaction potential, as long as this potential decays at large
distances faster than Kepler's inverse distance law. This leads to the
emergence of a new type of energetically-favourable quasiparticle: bielectron
vortices, which are double-charged and reside at zero-energy. Their bosonic
nature allows for condensation and may give rise to Majorana physics without
invoking a superconductor. These novel quasiparticles arguably explain a range
of poorly understood experiments in gated graphene structures at low doping.Comment: 9 pages, 2 figure
Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields
We show how it is possible to trap two-dimensional massless Dirac fermions in
spatially inhomogeneous magnetic fields, as long as the formed magnetic quantum
dot (or ring) is of a slowly decaying nature. It is found that a modulation of
the depth of the magnetic quantum dot leads to successive
confinement-deconfinement transitions of vortexlike states with a certain
angular momentum, until a regime is reached where only states with one sign of
angular momentum are supported. We illustrate these characteristics with both
exact solutions and a hitherto unknown quasi-exactly solvable model utilizing
confluent Heun functions.Comment: 7 pages, 3 figure
The economic ecology of small businesses in Oxfordshire
Report by the Oxfordshire Economic Observatory (OEO) for the Federation of Small Businesses (FSB), Oxfordshire Branch
Joint disease mapping using six cancers in the Yorkshire region of England
OBJECTIVES:
The aims of this study were to model jointly the incidence rates of six smoking related cancers in the Yorkshire region of England, to explore the patterns of spatial correlation amongst them, and to estimate the relative weight of smoking and other shared risk factors for the relevant disease sites, both before and after adjustment for socioeconomic background (SEB).
METHODS:
Data on the incidence of oesophagus, stomach, pancreas, lung, kidney, and bladder cancers between 1983 and 2003 were extracted from the Northern & Yorkshire Cancer Registry database for the 532 electoral wards in the Yorkshire region. Using postcode of residence, each case was assigned an area-based measure of SEB using the Townsend index. Standardised incidence ratios (SIRs) were calculated for each cancer site and their correlations investigated. The joint analysis of the spatial variation in incidence used a Bayesian shared-component model. Three components were included to represent differences in smoking (for all six sites), bodyweight/obesity (for oesophagus, pancreas and kidney cancers) and diet/alcohol consumption (for oesophagus and stomach cancers).
RESULTS:
The incidence of cancers of the oesophagus, pancreas, kidney, and bladder was relatively evenly distributed across the region. The incidence of stomach and lung cancers was more clustered around the urban areas in the south of the region, and these two cancers were significantly associated with higher levels of area deprivation. The incidence of lung cancer was most impacted by adjustment for SEB, with the rural/urban split becoming less apparent. The component representing smoking had a larger effect on cancer incidence in the eastern part of the region. The effects of the other two components were small and disappeared after adjustment for SEB.
CONCLUSIONS:
This study demonstrates the feasibility of joint disease modelling using data from six cancer sites. Incidence estimates are more precise than those obtained without smoothing. This methodology may be an important tool to help authorities evaluate healthcare system performance and the impact of policies
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