Carboranylmethylene-substituted phosphazenes and polymers thereof

Carboranylmethylene-substituted cyclophosphazenes are described which can be thermally polymerized into carboranylmethylene-substituted phosphazene polymers. The polymers are useful as thermally stable coatings. Also, due to the characteristics of these polymers in acting as a ligand for transition metals, metalocarboranylmethylene phosphazene polymers are described which can act as immobilized catalyst systems, and are electrically conductive and superconductive

Composite absorbing potentials

The multiple scattering interferences due to the addition of several contiguous potential units are used to construct composite absorbing potentials that absorb at an arbitrary set of incident momenta or for a broad momentum interval.Comment: 9 pages, Revtex, 2 postscript figures. Accepted in Phys. Rev. Let

Process for the preparation of polycarboranylphosphazenes

A process for the preparation of polycarboranylphosphazenes is described. Polydihalophosphazenes are allowed to react at ambient temperatures for at least one hour with a lithium carborane in a suitable inert solvent. The remaining chlorine substituents of the carboranyl polyphosphazene are then replaced with aryloxy or alkoxy groups to enhance moisture resistance. The polymers give a high char yield when exposed to extreme heat and flame and can be used as insulation

Carboranylcyclotriphosphazenes and their polymers

Carboranyl-substituted polyphosphazenes are prepared by heat polymerizing a carboranyl halocyclophosphazene at 250 C for about 120 hours in the absence of oxygen and moisture. The cyclophosphazene is obtained by allowing a lithium carborane, e.g., the reaction product of methyl-o-carborane with n-butyllithium in ethyl ether, to react with e.g., hexachlorocyclotriphosphazene at ambient temperatures and in anhydrous conditions. For greater stability in the presence of moisture, the chlorine substituents of the polymer are then replaced by aryloxy or alkoxy groups, such as CF3CH2O. The new substantially inorganic polymers are thermally stable materials which produce a high char yield when exposed to extreme temperatures, and can thus serve to insulate less heat and fire resistant substances

Quantum Time and Spatial Localization: An Analysis of the Hegerfeldt Paradox

Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles and dependence of spatial localization on the motion of the observer, are analyzed in the context of Dirac's theory of constraints. A parametrization invariant formulation is obtained by introducing time and energy operators for the relativistic particle and then treating the Klein-Gordon equation as a constraint. The standard, physical Hilbert space is recovered, via integration over proper time, from an augmented Hilbert space wherein time and energy are dynamical variables. It is shown that the Newton-Wigner position operator, being in this description a constant of motion, acts on states in the augmented space. States with strictly positive energy are non-local in time; consequently, position measurements receive contributions from states representing the particle's position at many times. Apparent superluminal propagation is explained by noting that, as the particle is potentially in the past (or future) of the assumed initial place and time of localization, it has time to propagate to distant regions without exceeding the speed of light. An inequality is proven showing the Hegerfeldt paradox to be completely accounted for by the hypotheses of subluminal propagation from a set of initial space-time points determined by the quantum time distribution arising from the positivity of the system's energy. Spatial localization can nevertheless occur through quantum interference between states representing the particle at different times. The non-locality of the same system to a moving observer is due to Lorentz rotation of spatial axes out of the interference minimum.Comment: This paper is identical to the version appearing in J. Math. Phys. 41; 6093 (Sept. 2000). The published version will be found at http://ojps.aip.org/jmp/. The paper (40 page PDF file) has been completely revised since the last posting to this archiv

Ambiguities of arrival-time distributions in quantum theory

We consider the definition that might be given to the time at which a particle arrives at a given place, both in standard quantum theory and also in Bohmian mechanics. We discuss an ambiguity that arises in the standard theory in three, but not in one, spatial dimension.Comment: LaTex, 12 pages, no figure

A measurement-based approach to quantum arrival times

For a quantum-mechanically spread-out particle we investigate a method for determining its arrival time at a specific location. The procedure is based on the emission of a first photon from a two-level system moving into a laser-illuminated region. The resulting temporal distribution is explicitly calculated for the one-dimensional case and compared with axiomatically proposed expressions. As a main result we show that by means of a deconvolution one obtains the well known quantum mechanical probability flux of the particle at the location as a limiting distribution.Comment: 11 pages, 4 figures, submitted to Phys. Rev.

Space-time properties of free motion time-of-arrival eigenstates

The properties of the time-of-arrival operator for free motion introduced by Aharonov and Bohm and of its self-adjoint variants are studied. The domains of applicability of the different approaches are clarified. It is shown that the arrival time of the eigenstates is not sharply defined. However, strongly peaked real-space (normalized) wave packets constructed with narrow Gaussian envelopes centred on one of the eigenstates provide an arbitrarily sharp arrival time.Comment: REVTEX, 12 pages, 4 postscript figure

Quantum times of arrival for multiparticle states

Using the concept of crossing state and the formalism of second quantization, we propose a prescription for computing the density of arrivals of particles for multiparticle states, both in the free and the interacting case. The densities thus computed are positive, covariant in time for time independent hamiltonians, normalized to the total number of arrivals, and related to the flux. We investigate the behaviour of this prescriptions for bosons and fermions, finding boson enhancement and fermion depletion of arrivals.Comment: 10 a4 pages, 5 inlined figure