3,411 research outputs found
Nonperturbative calculation of Born-Infeld effects on the Schroedinger spectrum of the hydrogen atom
We present the first nonperturbative numerical calculations of the
nonrelativistic hydrogen spectrum as predicted by first-quantized
electrodynamics with nonlinear Maxwell-Born-Infeld field equations. We also
show rigorous upper and lower bounds on the ground state.
When judged against empirical data our results significantly restrict the
range of viable values of the new electromagnetic constant which is introduced
by the Born-Infeld theory.
We assess Born's own proposal for the value of his constant.Comment: 4p., 2 figs, 1 table; submitted for publicatio
(Never) Mind your p's and q's: Von Neumann versus Jordan on the Foundations of Quantum Theory
In two papers entitled "On a new foundation [Neue Begr\"undung] of quantum
mechanics," Pascual Jordan (1927b,g) presented his version of what came to be
known as the Dirac-Jordan statistical transformation theory. As an alternative
that avoids the mathematical difficulties facing the approach of Jordan and
Paul A. M. Dirac (1927), John von Neumann (1927a) developed the modern Hilbert
space formalism of quantum mechanics. In this paper, we focus on Jordan and von
Neumann. Central to the formalisms of both are expressions for conditional
probabilities of finding some value for one quantity given the value of
another. Beyond that Jordan and von Neumann had very different views about the
appropriate formulation of problems in quantum mechanics. For Jordan, unable to
let go of the analogy to classical mechanics, the solution of such problems
required the identication of sets of canonically conjugate variables, i.e., p's
and q's. For von Neumann, not constrained by the analogy to classical
mechanics, it required only the identication of a maximal set of commuting
operators with simultaneous eigenstates. He had no need for p's and q's. Jordan
and von Neumann also stated the characteristic new rules for probabilities in
quantum mechanics somewhat differently. Jordan (1927b) was the first to state
those rules in full generality. Von Neumann (1927a) rephrased them and, in a
subsequent paper (von Neumann, 1927b), sought to derive them from more basic
considerations. In this paper we reconstruct the central arguments of these
1927 papers by Jordan and von Neumann and of a paper on Jordan's approach by
Hilbert, von Neumann, and Nordheim (1928). We highlight those elements in these
papers that bring out the gradual loosening of the ties between the new quantum
formalism and classical mechanics.Comment: New version. The main difference with the old version is that the
introduction has been rewritten. Sec. 1 (pp. 2-12) in the old version has
been replaced by Secs. 1.1-1.4 (pp. 2-31) in the new version. The paper has
been accepted for publication in European Physical Journal
Evaluation of Born and local effective charges in unoriented materials from vibrational spectra
We present an application of the Lorentz model in which fits to vibrational
spectra or a Kramers Kronig analysis are employed along with several useful
formalisms to quantify microscopic charge in unoriented (powdered) materials.
The conditions under which these techniques can be employed are discussed, and
we analyze the vibrational response of a layered transition metal
dichalcogenide and its nanoscale analog to illustrate the utility of this
approach.Comment: 9 pages, 1 figur
Imaging the Near Field
In an earlier paper we introduced the concept of the perfect lens which
focuses both near and far electromagnetic fields, hence attaining perfect
resolution. Here we consider refinements of the original prescription designed
to overcome the limitations of imperfect materials. In particular we show that
a multi-layer stack of positive and negative refractive media is less sensitive
to imperfections. It has the novel property of behaving like a fibre-optic
bundle but one that acts on the near field, not just the radiative component.
The effects of retardation are included and minimized by making the slabs
thinner. Absorption then dominates image resolution in the near-field. The
deleterious effects of absorption in the metal are reduced for thinner layers.Comment: RevTeX, (9 pages, 8 figures
Vibrations of closed-shell Lennard-Jones icosahedral and cuboctahedral clusters and their effect on the cluster ground state energy
Vibrational spectra of closed shell Lennard-Jones icosahedral and
cuboctahedral clusters are calculated for shell numbers between 2 and 9.
Evolution of the vibrational density of states with the cluster shell number is
examined and differences between icosahedral and cuboctahedral clusters
described. This enabled a quantum calculation of quantum ground state energies
of the clusters in the quasiharmonic approximation and a comparison of the
differences between the two types of clusters. It is demonstrated that in the
quantum treatment, the closed shell icosahedral clusters binding energies
differ from those of cuboctahedral clusters more than is the case in classical
treatment
Diffraction limit of the sub-Planck structures
The orthogonality of cat and displaced cat states, underlying Heisenberg
limited measurement in quantum metrology, is studied in the limit of large
number of states. The asymptotic expression for the corresponding state overlap
function, controlled by the sub-Planck structures arising from phase space
interference, is obtained exactly. The validity of large phase space support,
in which context the asymptotic limit is achieved, is discussed in detail. For
large number of coherent states, uniformly located on a circle, it identically
matches with the diffraction pattern for a circular ring with uniform angular
source strength. This is in accordance with the van Cittert-Zernike theorem,
where the overlap function, similar to the mutual coherence function matches
with a diffraction pattern.Comment: 5 pages, 3 figure
A General Approach to Casimir Force Problems Based on Local Reflection Amplitudes and Huygen's Principle
In this paper we describe an approach to Casimir Force problems that is
ultimately generalizable to all fields, boundary conditions, and cavity
geometries. This approach utilizes locally defined reflection amplitudes to
express the energy per unit area of any Casimir interaction. To demonstrate
this approach we solve a number of Casimir Force problems including the case of
uniaxial boundary conditions in a parallel-plate cavity.Comment: 9 pages, 5 figures, Equation 18 has been corrected, [v1] contained a
typ
Inelastic Diffraction and Spectroscopy of Very Weakly Bound Clusters
We study the coherent inelastic diffraction of very weakly bound two body
clusters from a material transmission grating. We show that internal
transitions of the clusters can lead to new separate peaks in the diffraction
pattern whose angular positions determine the excitation energies. Using a
quantum mechanical approach to few body scattering theory we determine the
relative peak intensities for the diffraction of the van der Waals dimers
(D_2)_2 and H_2-D_2. Based on the results for these realistic examples we
discuss the possible applications and experimental challenges of this coherent
inelastic diffraction technique.Comment: 15 pages + 5 figures. J. Phys. B (in press
Perfect imaging with positive refraction in three dimensions
Maxwell's fish eye has been known to be a perfect lens within the validity
range of ray optics since 1854. Solving Maxwell's equations we show that the
fish-eye lens in three dimensions has unlimited resolution for electromagnetic
waves
Sexual Orientation Among Men Associated with Christian Groups: A Discriminant Analysis
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