79,231 research outputs found
Improved eigenvalue bounds for Schr\"odinger operators with slowly decaying potentials
We extend a result of Davies and Nath on the location of eigenvalues of
Schr\"odinger operators with slowly decaying complex-valued potentials to
higher dimensions. In this context, we also discuss various examples related to
the Laptev--Safronov conjecture.Comment: Some typos correcte
Spectral theory of a mathematical model in Quantum Field Theory for any spin
In this paper we use the formalism of S.Weinberg in order to construct a
mathematical model based on the weak decay of hadrons and nuclei. In particular
we consider a model which generalizes the weak decay of the nucleus of the
cobalt. We associate with this model a Hamiltonian with cutoffs in a Fock
space. The Hamiltonian is self-adjoint and has an unique ground state. By using
the commutator theory we get a limiting absorption principle from which we
deduce that the spectrum of the Hamiltonian is absolutely continuous above the
energy of the ground state and below the first threshold.Comment: A subsection revise
Bounds on primitives of differential forms and cofilling inequalities
We prove that on a Riemannian manifold, a smooth differential form has a
primitive with a given (functional) upper bound provided the necessary weighted
isoperimetric inequalities implied by Stokes are satisfied. We apply this to
prove a comparison predicted by Gromov between the cofilling function and the
filling area.Comment: The new features of the main result are its sharpness and the fact
that the manifold is not assumed have bounded geometry, nor even to be
complete. This paper corresponds to a part of a talk given in January 2004 in
Haifa, at a workshop in memory of Robert Brooks. The other part, which is the
"translation" in the framework of geometric group theory, will soon be
deposited on arxi
Sequences of Exact Analytical Solutions for Plane-Waves in Graded Media
We present a new method for building sequences of solvable profiles of the
electromagnetic (EM) admittance in lossless isotropic materials with 1D graded
permittivity and permeability (in particular profiles of the optical
refractive-index). These solvable profiles lead to analytical closed-form
expressions of the EM fields, for both TE and TM modes. The Property-and-Field
Darboux Transformations method, initially developed for heat diffusion
modelling, is here transposed to the Maxwell equations in the optical-depth
space. Several examples are provided, all stemming from a constant
seed-potential, which makes them based on elementary functions only. Solvable
profiles of increasingly complex shape can be obtained by iterating the process
or by assembling highly flexible canonical profiles. Their implementation for
modelling optical devices like matching layers, rugate filters, Bragg gratings,
chirped mirrors or 1D photonic crystals, offers an exact and cost-effective
alternative to the classical approachesComment: 74 pages, 20 figures, Corrected typos in Annex
Dual elliptic structures on CP2
We consider an almost complex structure J on CP2, or more generally an
elliptic structure E which is tamed by the standard symplectic structure. An
E-curve is a surface tangent to E (this generalizes the notion of
J(holomorphic)-curve), and an E-line is an E-curve of degree 1. We prove that
the space of E-lines is again a CP2 with a tame elliptic structure E^*, and
that each E-curve has an associated dual E^*-curve. This implies that the
E-curves, and in particular the J-curves, satisfy the Pl\"ucker formulas, which
restricts their possible sets of singularities.Comment: 18 pages The only difference with the first version is the mention of
the thesis of Benjamin MacKay ("Duality and integrable systems of
pseudoholomorphic curves", Duke University, 1999), which I did not know at
the time, and which contains a large part of the results of my pape
Geometric descriptions of polygon and chain spaces
We give a few simple methods to geometically describe some polygon and
chain-spaces in R^d. They are strong enough to give tables of m-gons and
m-chains when m <= 6
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