3,180 research outputs found
Distinguished Cp(X) spaces
We continue our initial study of Cp(X) spaces that are distinguished, equiv., are large subspaces
of RX , equiv., whose strong duals Lβ(X) carry the strongest locally convex topology.
Many are distinguished, many are not. All Lβ(X) spaces are, as are all metrizable Cp(X)
and Ck (X) spaces. To prove a space Cp(X) is not distinguished, we typically compare the
character of Lβ(X) with |X|. A certain covering for X we call a scant cover is used to find
distinguished Cp(X) spaces. Two of the main results are: (i) Cp(X) is distinguished if and
only if its bidual E coincides with RX , and (ii) for a Corson compact space X, the space
Cp(X) is distinguished if and only if X is scattered and Eberlein compact
Exact results for `bouncing' Gaussian wave packets
We consider time-dependent Gaussian wave packet solutions of the Schrodinger
equation (with arbitrary initial central position, x_0, and momentum, p_0, for
an otherwise free-particle, but with an infinite wall at x=0, so-called
bouncing wave packets. We show how difference or mirror solutions of the form
psi(x,t)-psi(-x,t) can, in this case, be normalized exactly, allowing for the
evaluation of a number of time-dependent expectation values and other
quantities in closed form. For example, we calculate _t explicitly which
illustrates how the free-particle kinetic (and hence total) energy is affected
by the presence of the distant boundary. We also discuss the time dependence of
the expectation values of position, _t, and momentum, _t, and their
relation to the impulsive force during the `collision' with the wall. Finally,
the x_0,p_0 --> 0 limit is shown to reduce to a special case of a non-standard
free-particle Gaussian solution. The addition of this example to the literature
then expands on the relatively small number of Gaussian solutions to quantum
mechanical problems with familiar classical analogs (free particle, uniform
acceleration, harmonic oscillator, unstable oscillator, and uniform magnetic
field) available in closed form.Comment: 14 pages, 1 embedded .eps figur
The Stark effect in linear potentials
We examine the Stark effect (the second-order shift in the energy spectrum
due to an external constant force) for two 1-dimensional model quantum
mechanical systems described by linear potentials, the so-called quantum
bouncer (defined by V(z) = Fz for z>0 and V(z) infinite for z<0) and the
symmetric linear potential (given by V(z) = F|z|). We show how straightforward
use of the most obvious properties of the Airy function solutions and simple
Taylor expansions give closed form results for the Stark shifts in both
systems. These exact results are then compared to other approximation
techniques, such as perturbation theory and WKB methods. These expressions add
to the small number of closed-form descriptions available for the Stark effect
in model quantum mechanical systems.Comment: 15 pages. To appear in Eur. J. Phys. Needs Institute of Physics
(iopart) style file
Eikonal analysis of Coulomb distortion in quasi-elastic electron scattering
An eikonal expansion is used to provide systematic corrections to the eikonal
approximation through order , where is the wave number. Electron
wave functions are obtained for the Dirac equation with a Coulomb potential.
They are used to investigate distorted-wave matrix elements for quasi-elastic
electron scattering from a nucleus. A form of effective-momentum approximation
is obtained using trajectory-dependent eikonal phases and focusing factors.
Fixing the Coulomb distortion effects at the center of the nucleus, the
often-used ema approximation is recovered. Comparisons of these approximations
are made with full calculations using the electron eikonal wave functions. The
ema results are found to agree well with the full calculations.Comment: 12 pages, 6 Postscript figure
Strange Decays of Nonstrange Baryons
The strong decays of excited nonstrange baryons into the final states Lambda
K, Sigma K, and for the first time into Lambda(1405) K, Lambda(1520) K,
Sigma(1385) K, Lambda K*, and Sigma K*, are examined in a relativized quark
pair creation model. The wave functions and parameters of the model are fixed
by previous calculations of N pi and N pi pi, etc., decays. Our results show
that it should be possible to discover several new negative parity excited
baryons and confirm the discovery of several others by analyzing these final
states in kaon production experiments. We also establish clear predictions for
the relative strengths of certain states to decay to Lambda(1405) K and
Lambda(1520) K, which can be tested to determine if a three-quark model of the
Lambda(1405) K is valid. Our results compare favorably with the results of
partial wave analyses of the limited existing data for the Lambda K and Sigma K
channels. We do not find large Sigma K decay amplitudes for a substantial group
of predicted and weakly established negative-parity states, in contrast to the
only previous work to consider decays of these states into the strange final
states Lambda K and Sigma K.Comment: 25 pages, 8 figures, RevTe
Weak localization of light by cold atoms: the impact of quantum internal structure
Since the work of Anderson on localization, interference effects for the
propagation of a wave in the presence of disorder have been extensively
studied, as exemplified in coherent backscattering (CBS) of light. In the
multiple scattering of light by a disordered sample of thermal atoms,
interference effects are usually washed out by the fast atomic motion. This is
no longer true for cold atoms where CBS has recently been observed. However,
the internal structure of the atoms strongly influences the interference
properties. In this paper, we consider light scattering by an atomic dipole
transition with arbitrary degeneracy and study its impact on coherent
backscattering. We show that the interference contrast is strongly reduced.
Assuming a uniform statistical distribution over internal degrees of freedom,
we compute analytically the single and double scattering contributions to the
intensity in the weak localization regime. The so-called ladder and crossed
diagrams are generalized to the case of atoms and permit to calculate
enhancement factors and backscattering intensity profiles for polarized light
and any closed atomic dipole transition.Comment: 22 pages Revtex, 9 figures, to appear in PR
Analytic results for Gaussian wave packets in four model systems: I. Visualization of the kinetic energy
Using Gaussian wave packet solutions, we examine how the kinetic energy is
distributed in time-dependent solutions of the Schrodinger equation
corresponding to the cases of a free particle, a particle undergoing uniform
acceleration, a particle in a harmonic oscillator potential, and a system
corresponding to an unstable equilibrium. We find, for specific choices of
initial parameters, that as much as 90% of the kinetic energy can be localized
(at least conceptually) in the `front half' of such Gaussian wave packets, and
we visualize these effects.Comment: 22 pages, RevTeX, four .eps figures, to appear in Found. Phys. Lett.
Vol. 17, Dec. 200
Investigating the social value of the Ripon rivers flood alleviation scheme
This paper argues for an approach to flood alleviation design that considers the need not only for technical knowledge, but also a social perspective. It is predicted that more intense rainfall and rising sea levels will result in a greater number of people vulnerable to flood events. Flood alleviation design in the UK is often focused upon technical and cost-effective solutions, and consideration of social impact is seen as secondary. This paper examines how the social value of a UK flood alleviation scheme is perceived and discussed, by the local community and by those responsible for the design of the scheme, and exposes differences in perceptions both between and within these two groups. It recommends a future approach in which an understanding of the social value of a flood alleviation scheme is first co-produced with the community affected, enabling the design of a socially acceptable and successful project.The research presented in this paper is part of a larger study. The research is conducted with the aid of funding from an Engineering and Physical Sciences Research Council (EPSRC) iCASE doctoral award. Ove Arup and Partners also provide sponsorship as part of the award.This is the final version of the article. It first appeared from Wiley via http://dx.doi.org/10.1111/jfr3.1217
Combined QCD and electroweak analysis of HERA data
A simultaneous fit of parton distribution functions (PDFs) and electroweak
parameters to HERA data on deep inelastic scattering is presented. The input
data are the neutral current and charged current inclusive cross sections which
were previously used in the QCD analysis leading to the HERAPDF2.0 PDFs. In
addition, the polarisation of the electron beam was taken into account for the
ZEUS data recorded between 2004 and 2007. Results on the vector and
axial-vector couplings of the Z boson to u- and d-type quarks, on the value of
the electroweak mixing angle and the mass of the W boson are presented. The
values obtained for the electroweak parameters are in agreement with Standard
Model predictions.Comment: 32 pages, 10 figures, accepted by Phys. Rev. D. Small corrections
from proofing process and small change to Fig. 12 and Table
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