4,395 research outputs found
The Charge-Transfer Motif in Crystal Engineering. Self-Assembly of Acentric (Diamondoid) Networks from Halide Salts and Carbon Tetrabromide as Electron-Donor/Acceptor Synthons
Unusual strength and directionality for the charge-transfer motif (established in solution) are shown to carry over into the solid state by the facile synthesis of a series of robust crystals of the [1:1] donor/acceptor complexes of carbon tetrabromide with the electron-rich halide anions (chloride, bromide, and iodide). X-ray crystallographic analyses identify the consistent formation of diamondoid networks, the dimensionality of which is dictated by the size of the tetraalkylammonium counterion. For the tetraethylammonium bromide/carbon tetrabromide dyad, the three-dimensional (diamondoid) network consists of donor (bromide) and acceptor (CBr4) nodes alternately populated to result in the effective annihilation of centers of symmetry in agreement with the sphaleroid structural subclass. Such inherently acentric networks exhibit intensive nonlinear optical properties in which the second harmonics generation in the extended charge-transfer system is augmented by the effective electronic (HOMO−LUMO) coupling between contiguous CBr4/halide centers
Representation Theory Approach to the Polynomial Solutions of q - Difference Equations : U_q(sl(3)) and Beyond,
A new approach to the theory of polynomial solutions of q - difference
equations is proposed. The approach is based on the representation theory of
simple Lie algebras and their q - deformations and is presented here for
U_q(sl(n)). First a q - difference realization of U_q(sl(n)) in terms of
n(n-1)/2 commuting variables and depending on n-1 complex representation
parameters r_i, is constructed. From this realization lowest weight modules
(LWM) are obtained which are studied in detail for the case n=3 (the well known
n=2 case is also recovered). All reducible LWM are found and the polynomial
bases of their invariant irreducible subrepresentations are explicitly given.
This also gives a classification of the quasi-exactly solvable operators in the
present setting. The invariant subspaces are obtained as solutions of certain
invariant q - difference equations, i.e., these are kernels of invariant q -
difference operators, which are also explicitly given. Such operators were not
used until now in the theory of polynomial solutions. Finally the states in all
subrepresentations are depicted graphically via the so called Newton diagrams.Comment: uuencoded Z-compressed .tar file containing two ps files
Pair creation and plasma oscillations
We describe aspects of particle creation in strong fields using a quantum
kinetic equation with a relaxation-time approximation to the collision term.
The strong electric background field is determined by solving Maxwell's
equation in tandem with the Vlasov equation. Plasma oscillations appear as a
result of feedback between the background field and the field generated by the
particles produced. The plasma frequency depends on the strength of the initial
background field and the collision frequency, and is sensitive to the necessary
momentum-dependence of dressed-parton masses.Comment: 11 pages, revteX, epsfig.sty, 5 figures; Proceedings of 'Quark Matter
in Astro- and Particlephysics', a workshop at the University of Rostock,
Germany, November 27 - 29, 2000. Eds. D. Blaschke, G. Burau, S.M. Schmid
Phase Space Evolution and Discontinuous Schr\"odinger Waves
The problem of Schr\"odinger propagation of a discontinuous wavefunction
-diffraction in time- is studied under a new light. It is shown that the
evolution map in phase space induces a set of affine transformations on
discontinuous wavepackets, generating expansions similar to those of wavelet
analysis. Such transformations are identified as the cause for the
infinitesimal details in diffraction patterns. A simple case of an evolution
map, such as SL(2) in a two-dimensional phase space, is shown to produce an
infinite set of space-time trajectories of constant probability. The
trajectories emerge from a breaking point of the initial wave.Comment: Presented at the conference QTS7, Prague 2011. 12 pages, 7 figure
Mesoscopic to universal crossover of transmission phase of multi-level quantum dots
Transmission phase \alpha measurements of many-electron quantum dots (small
mean level spacing \delta) revealed universal phase lapses by \pi between
consecutive resonances. In contrast, for dots with only a few electrons (large
\delta), the appearance or not of a phase lapse depends on the dot parameters.
We show that a model of a multi-level quantum dot with local Coulomb
interactions and arbitrary level-lead couplings reproduces the generic features
of the observed behavior. The universal behavior of \alpha for small \delta
follows from Fano-type antiresonances of the renormalized single-particle
levels.Comment: 4 pages, version accepted for publication in PR
Average transmission probability of a random stack
The transmission through a stack of identical slabs that are separated by
gaps with random widths is usually treated by calculating the average of the
logarithm of the transmission probability. We show how to calculate the average
of the transmission probability itself with the aid of a recurrence relation
and derive analytical upper and lower bounds. The upper bound, when used as an
approximation for the transmission probability, is unreasonably good and we
conjecture that it is asymptotically exact.Comment: 10 pages, 6 figure
Influence of radiative damping on the optical-frequency susceptibility
Motivated by recent discussions concerning the manner in which damping
appears in the electric polarizability, we show that (a) there is a dependence
of the nonresonant contribution on the damping and that (b) the damping enters
according to the "opposite sign prescription." We also discuss the related
question of how the damping rates in the polarizability are related to
energy-level decay rates
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