263 research outputs found
The Structure of Polyfulvenes
Cationic polymerisation of 6,6-disubstituted pentafulvenes
yields highly unsaturated, reactive macromolecules of high mo- .
lecular weight. The mechanistic pathways leading to the polymers
are discussed, and the structure XIV of the polymers has been
elucidated by a combination of spectroscopic methods as well as by
comparison with model compounds. In contrast to reports in the
literature, the main process in thermal oligomerisation of simple
pentafulvenes at 20 °c is a Diels-Alder reaction giving products of
type XXI. Anionic polymerisation of pentafulvenes is initiated by
traces of sodium cyclopentadienide or phenylsodium respectively.
The reaction products consist of a mixture of oligomers of the
series (fulvene)n. This surprising result can be explained by structure
elucidation of the fulvene dimers, which gives formula XX.
The mechanistic aspects of the reaction are discussed
Dispersive estimates for Schr\"odinger operators with point interactions in
The study of dispersive properties of Schr\"odinger operators with point
interactions is a fundamental tool for understanding the behavior of many body
quantum systems interacting with very short range potential, whose dynamics can
be approximated by non linear Schr\"odinger equations with singular
interactions. In this work we proved that, in the case of one point interaction
in , the perturbed Laplacian satisfies the same
estimates of the free Laplacian in the smaller regime . These
estimates are implied by a recent result concerning the boundedness of
the wave operators for the perturbed Laplacian. Our approach, however, is more
direct and relatively simple, and could potentially be useful to prove optimal
weighted estimates also in the regime .Comment: To appear on: "Advances in Quantum Mechanics: Contemporary Trends and
Open Problems", G. Dell'Antonio and A. Michelangeli eds., Springer-INdAM
series 201
Enhanced suppresion of localization in a continuous Random-Dimer Model
We consider a one-dimensional continuous (Kronig-Penney) extension of the
(tight-binding) Random Dimer model of Dunlap et al. [Phys. Rev. Lett. 65, 88
(1990)]. We predict that the continuous model has infinitely many resonances
(zeroes of the reflection coefficient) giving rise to extended states instead
of the one resonance arising in the discrete version. We present exact,
transfer-matrix numerical calculations supporting, both realizationwise and on
the average, the conclusion that the model has a very large number of extended
states.Comment: 10 pages, 3 Figures available on request, REVTeX 3.0, MA/UC3M/1/9
Proper incorporation of self-adjoint extension method to Green's function formalism : one-dimensional -function potential case
One-dimensional -function potential is discussed in the framework
of Green's function formalism without invoking perturbation expansion. It is
shown that the energy-dependent Green's function for this case is crucially
dependent on the boundary conditions which are provided by self-adjoint
extension method. The most general Green's function which contains four real
self-adjoint extension parameters is constructed. Also the relation between the
bare coupling constant and self-adjoint extension parameter is derived.Comment: LATEX, 13 page
Dimensional crossover of a boson gas in multilayers
We obtain the thermodynamic properties for a non-interacting Bose gas
constrained on multilayers modeled by a periodic Kronig-Penney delta potential
in one direction and allowed to be free in the other two directions. We report
Bose-Einstein condensation (BEC) critical temperatures, chemical potential,
internal energy, specific heat, and entropy for different values of a
dimensionless impenetrability between layers. The BEC critical
temperature coincides with the ideal gas BEC critical temperature
when and rapidly goes to zero as increases to infinity for
any finite interlayer separation. The specific heat \textit{vs} for
finite and plane separation exhibits one minimum and one or two maxima
in addition to the BEC, for temperatures larger than which highlights
the effects due to particle confinement. Then we discuss a distinctive
dimensional crossover of the system through the specific heat behavior driven
by the magnitude of . For the crossover is revealed by the change
in the slope of and when , it is evidenced by a broad
minimum in .Comment: Ten pages, nine figure
Can Light Signals Travel Faster than c in Nontrivial Vacuua in Flat space-time? Relativistic Causality II
In this paper we show that the Scharnhorst effect (Vacuum with boundaries or
a Casimir type vacuum) cannot be used to generate signals showing measurable
faster-than-c speeds. Furthermore, we aim to show that the Scharnhorst effect
would violate special relativity, by allowing for a variable speed of light in
vacuum, unless one can specify a small invariant length scale. This invariant
length scale would be agreed upon by all inertial observers. We hypothesize the
approximate scale of the invariant length.Comment: 12 pages no figure
Exact particle and kinetic energy densities for one-dimensional confined gases of non-interacting fermions
We propose a new method for the evaluation of the particle density and
kinetic pressure profiles in inhomogeneous one-dimensional systems of
non-interacting fermions, and apply it to harmonically confined systems of up
to N=1000 fermions. The method invokes a Green's function operator in
coordinate space, which is handled by techniques originally developed for the
calculation of the density of single-particle states from Green's functions in
the energy domain. In contrast to the Thomas-Fermi (local density)
approximation, the exact profiles under harmonic confinement show negative
local pressure in the tails and a prominent shell structure which may become
accessible to observation in magnetically trapped gases of fermionic alkali
atoms.Comment: 8 pages, 3 figures, accepted for publication in Phys. Rev. Let
On the Green function of linear evolution equations for a region with a boundary
We derive a closed-form expression for the Green function of linear evolution
equations with the Dirichlet boundary condition for an arbitrary region, based
on the singular perturbation approach to boundary problems.Comment: 9 page
Resonance-Induced Effects in Photonic Crystals
For the case of a simple face-centered-cubic photonic crystal of homogeneous
dielectric spheres, we examine to what extent single-sphere Mie resonance
frequencies are related to band gaps and whether the width of a gap can be
enlarged due to nearby resonances. Contrary to some suggestions, no spectacular
effects may be expected. When the dielectric constant of the spheres
is greater than the dielectric constant of the
background medium, then for any filling fraction there exists a critical
above which the lowest lying Mie resonance frequency falls inside
the lowest stop gap in the (111) crystal direction, close to its midgap
frequency. If , the correspondence between Mie
resonances and both the (111) stop gap and a full gap does not follow such a
regular pattern. If the Mie resonance frequency is close to a gap edge, one can
observe a resonance-induced widening of a relative gap width by .Comment: 14 pages, 3 figs., RevTex. For more info look at
http://www.amolf.nl/external/wwwlab/atoms/theory/index.htm
The Structure of Polyfulvenes
Cationic polymerisation of 6,6-disubstituted pentafulvenes
yields highly unsaturated, reactive macromolecules of high mo- .
lecular weight. The mechanistic pathways leading to the polymers
are discussed, and the structure XIV of the polymers has been
elucidated by a combination of spectroscopic methods as well as by
comparison with model compounds. In contrast to reports in the
literature, the main process in thermal oligomerisation of simple
pentafulvenes at 20 °c is a Diels-Alder reaction giving products of
type XXI. Anionic polymerisation of pentafulvenes is initiated by
traces of sodium cyclopentadienide or phenylsodium respectively.
The reaction products consist of a mixture of oligomers of the
series (fulvene)n. This surprising result can be explained by structure
elucidation of the fulvene dimers, which gives formula XX.
The mechanistic aspects of the reaction are discussed
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