Synthesis and evaluation of polymers for use in early warning fire alarm devices

Conjugated polyacetylene polymers and one condensation polyene, all containing a high degree of conjugated unsaturation, were synthesized. These polymers were characterized by chemical analysis and by thermogravimetric analysis, as well as for their film-forming capability and gas/polymer interactions. It was found that those that had a high degree of conjugated unsaturation and had resonance - stabilizing groups were very thermally stable to 200 C, e.g., poly(dicyanoacetylene), poly(ethynylferrocene) and poly(phenylacetylene); while those with labile moieties, such as poly(p-formamidophenylacetylene), among others, suffered some degradation when heated in air. When subjected to gas/polymer interaction effects, the greatest change in electrical conductance was observed when ammonia was used as the gas and poly(p-nitrophenylacetylene) was the detector. Other polymers showed similar behavior. For example, poly(ethynylcarborane), considered to be an electron acceptor also showed a change in electrical conductance when exposed to ammonia, while poly(ethynylpyridine) and poly(ethylidenepyridazine) responded to carbon monoxide. However, for "fire gases" (gases from smoldering cotton), poly(ethynylferrocene) was the most responsive. Thus, the concept of polymers with different electronegativities forming charge-transfer complexes with different gases was found to be operable

Semiconducting polymers for gas detection

Conjugated polyenes, and polyesters containing phthalocyanine in their backbone, were synthesized. These polymers were characterized by chemical analysis, thermogravimetric analysis, spectral analysis, and X-ray diffraction studies for crystallinity, as well as for their film-forming capability and gas/polymer interactions. Most of the polymers were relatively insensitive to water vapor up to 50 percent relative humidity, but the polyester/phthalocyanine (iron) polymer was relatively insensitive up to 100 percent RH. On the other hand, poly(p-dimethylaminophenylacetylene) was too conductive at 100 percent RH. Of the gases tested, the only ones that gave any evidence of interacting with the polymers were SO2, NOx, HCN and NH3. Poly(imidazole)/thiophene responded to each of these gases at all relative humidities, while the other polymers gave varying response, depending upon the RH. Thus, since most of these gases were electron-accepting, the electron-donating character of poly(imidazole)/thiophene substantiates the concept of electronegativity being the operating principle for interaction effects. Of the six polymers prepared, poly(imidazole)/thiophene first showed a very good response to smoldering cotton, but it later became nonresponsive; presumably due to oxidation effects

Topological structures of adiabatic phase for multi-level quantum systems

The topological properties of adiabatic gauge fields for multi-level (three-level in particular) quantum systems are studied in detail. Similar to the result that the adiabatic gauge field for SU(2) systems (e.g. two-level quantum system or angular momentum systems, etc) have a monopole structure, the curvature two-forms of the adiabatic holonomies for SU(3) three-level and SU(3) eight-level quantum systems are shown to have monopole-like (for all levels) or instanton-like (for the degenerate levels) structures.Comment: 15 pages, no figures. Accepted by J.Phys.

A Parametrization of Bipartite Systems Based on SU(4) Euler Angles

In this paper we give an explicit parametrization for all two qubit density matrices. This is important for calculations involving entanglement and many other types of quantum information processing. To accomplish this we present a generalized Euler angle parametrization for SU(4) and all possible two qubit density matrices. The important group-theoretical properties of such a description are then manifest. We thus obtain the correct Haar (Hurwitz) measure and volume element for SU(4) which follows from this parametrization. In addition, we study the role of this parametrization in the Peres-Horodecki criteria for separability and its corresponding usefulness in calculating entangled two qubit states as represented through the parametrization.Comment: 23 pages, no figures; changed title and abstract and rewrote certain areas in line with referee comments. To be published in J. Phys. A: Math. and Ge

Explicitly symmetrical treatment of three-body phase space

We derive expressions for three-body phase space that are explicitly symmetrical in the masses of the three particles. We study geometrical properties of the variables involved in elliptic integrals and demonstrate that it is convenient to use the Jacobian zeta function to express the results in four and six dimensions.Comment: 20 pages, latex, 2 postscript figure

Finite-level systems, Hermitian operators, isometries, and a novel parameterization of Stiefel and Grassmann manifolds

In this paper we obtain a description of the Hermitian operators acting on the Hilbert space \C^n, description which gives a complete solution to the over parameterization problem. More precisely we provide an explicit parameterization of arbitrary $n$-dimensional operators, operators that may be considered either as Hamiltonians, or density matrices for finite-level quantum systems. It is shown that the spectral multiplicities are encoded in a flag unitary matrix obtained as an ordered product of special unitary matrices, each one generated by a complex $n-k$-dimensional unit vector, $k=0,1,...,n-2$. As a byproduct, an alternative and simple parameterization of Stiefel and Grassmann manifolds is obtained.Comment: 21 page

Calculation of the unitary part of the Bures measure for N-level quantum systems

We use the canonical coset parameterization and provide a formula with the unitary part of the Bures measure for non-degenerate systems in terms of the product of even Euclidean balls. This formula is shown to be consistent with the sampling of random states through the generation of random unitary matrices