3,914 research outputs found
Connection Conditions and the Spectral Family under Singular Potentials
To describe a quantum system whose potential is divergent at one point, one
must provide proper connection conditions for the wave functions at the
singularity. Generalizing the scheme used for point interactions in one
dimension, we present a set of connection conditions which are well-defined
even if the wave functions and/or their derivatives are divergent at the
singularity. Our generalized scheme covers the entire U(2) family of
quantizations (self-adjoint Hamiltonians) admitted for the singular system. We
use this scheme to examine the spectra of the Coulomb potential and the harmonic oscillator with square inverse potential , and thereby provide a general perspective for these
models which have previously been treated with restrictive connection
conditions resulting in conflicting spectra. We further show that, for any
parity invariant singular potentials , the spectrum is determined
solely by the eigenvalues of the characteristic matrix .Comment: TeX, 18 page
Classification of double flag varieties of complexity 0 and 1
A classification of double flag varieties of complexity 0 and 1 is obtained.
An application of this problem to decomposing tensor products of irreducible
representations of semisimple Lie groups is considered
A reduced subduction graph and higher multiplicity in S_n transformation coefficients
Transformation coefficients between {\it standard} bases for irreducible
representations of the symmetric group and {\it split} bases adapted to
the subgroup () are
considered. We first provide a \emph{selection rule} and an \emph{identity
rule} for the subduction coefficients which allow to decrease the number of
unknowns and equations arising from the linear method by Pan and Chen. Then,
using the {\it reduced subduction graph} approach, we may look at higher
multiplicity instances. As a significant example, an orthonormalized solution
for the first multiplicity-three case, which occurs in the decomposition of the
irreducible representation of into
of , is presented and discussed.Comment: 12 pages, 1 figure, iopart class, Revisited version (several
typographical errors have been corrected). Accepted for publication in J.
Phys. A: Math. Ge
Spectroscopy of Ne for the thermonuclear O()Ne and F()O reaction rates
Uncertainties in the thermonuclear rates of the
O()Ne and F()O reactions
affect model predictions of light curves from type I X-ray bursts and the
amount of the observable radioisotope F produced in classical novae,
respectively. To address these uncertainties, we have studied the nuclear
structure of Ne over MeV and MeV using
the F(He,t)Ne reaction. We find the values of the
4.14 and 4.20 MeV levels to be consistent with and
respectively, in contrast to previous assumptions. We confirm the recently
observed triplet of states around 6.4 MeV, and find evidence that the state at
6.29 MeV, just below the proton threshold, is either broad or a doublet. Our
data also suggest that predicted but yet unobserved levels may exist near the
6.86 MeV state. Higher resolution experiments are urgently needed to further
clarify the structure of Ne around the proton threshold before a
reliable F()O rate for nova models can be determined.Comment: 5 pages, 3 figures, Phys. Rev. C (in press
Hirzebruch-Milnor classes and Steenbrink spectra of certain projective hypersurfaces
We show that the Hirzebruch-Milnor class of a projective hypersurface, which
gives the difference between the Hirzebruch class and the virtual one, can be
calculated by using the Steenbrink spectra of local defining functions of the
hypersurface if certain good conditions are satisfied, e.g. in the case of
projective hyperplane arrangements, where we can give a more explicit formula.
This is a natural continuation of our previous paper on the Hirzebruch-Milnor
classes of complete intersections.Comment: 15 pages, Introduction is modifie
Bound-State Variational Wave Equation For Fermion Systems In QED
We present a formulation of the Hamiltonian variational method for QED which
enables the derivation of relativistic few-fermion wave equation that can
account, at least in principle, for interactions to any order of the coupling
constant. We derive a relativistic two-fermion wave equation using this
approach. The interaction kernel of the equation is shown to be the generalized
invariant M-matrix including all orders of Feynman diagrams. The result is
obtained rigorously from the underlying QFT for arbitrary mass ratio of the two
fermions. Our approach is based on three key points: a reformulation of QED,
the variational method, and adiabatic hypothesis. As an application we
calculate the one-loop contribution of radiative corrections to the two-fermion
binding energy for singlet states with arbitrary principal quantum number ,
and . Our calculations are carried out in the explicitly covariant
Feynman gauge.Comment: 26 page
Toda Fields on Riemann Surfaces: remarks on the Miura transformation
We point out that the Miura transformation is related to a holomorphic
foliation in a relative flag manifold over a Riemann Surface. Certain
differential operators corresponding to a free field description of
--algebras are thus interpreted as partial connections associated to the
foliation.Comment: AmsLatex 1.1, 10 page
New Approaches to HSCT Multidisciplinary Design and Optimization
The successful development of a capable and economically viable high speed civil transport (HSCT) is perhaps one of the most challenging tasks in aeronautics for the next two decades. At its heart it is fundamentally the design of a complex engineered system that has significant societal, environmental and political impacts. As such it presents a formidable challenge to all areas of aeronautics, and it is therefore a particularly appropriate subject for research in multidisciplinary design and optimization (MDO). In fact, it is starkly clear that without the availability of powerful and versatile multidisciplinary design, analysis and optimization methods, the design, construction and operation of im HSCT simply cannot be achieved. The present research project is focused on the development and evaluation of MDO methods that, while broader and more general in scope, are particularly appropriate to the HSCT design problem. The research aims to not only develop the basic methods but also to apply them to relevant examples from the NASA HSCT R&D effort. The research involves a three year effort aimed first at the HSCT MDO problem description, next the development of the problem, and finally a solution to a significant portion of the problem
Quantum simulations under translational symmetry
We investigate the power of quantum systems for the simulation of Hamiltonian
time evolutions on a cubic lattice under the constraint of translational
invariance. Given a set of translationally invariant local Hamiltonians and
short range interactions we determine time evolutions which can and those that
can not be simulated. Whereas for general spin systems no finite universal set
of generating interactions is shown to exist, universality turns out to be
generic for quadratic bosonic and fermionic nearest-neighbor interactions when
supplemented by all translationally invariant on-site Hamiltonians.Comment: 9 pages, 2 figures, references added, minor change
New Approaches to Multidisciplinary Design and Optimization
Research under the subject grant is being carried out in a jointly coordinated effort within three laboratories in the School of Aerospace Engineering and the George Woodruff School of Mechanical Engineering. The objectives and results for Year 2 of the research program are summarized. The "Objectives" and "Expected Significance" are taken directly from the Year 2 Proposal presented in October 1994, and "Results" summarize the what has been accomplished this year. A discussion of these results is provided in the following sections. A listing of papers, presentations and reports that acknowledge grant support, either in part or in whole, and that were prepared during this period is provided in an attachment
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