A methodology for current density calculations in high-frequency RF resonators

As nuclear magnetic resonance imaging and spectroscopy move inexorably toward higher field-strength magnets in search of improved signal-to-noise ratio, spectral resolution, and spatial resolution, the way in which radiofrequency (RF) probes are designed changes. At higher frequencies, resonant cavities become the favored RF ''coil'' type and may be built using streamline elements to reduce the inductance of the system. In modeling such systems, the quasi-static approach of assuming that current flows evenly in all conductor cross sections and that adjacent conductors do not affect each other becomes less reasonable. The proximity of RF conductors in resonators typically causes RF eddy currents to flow, whereby the current density in each rung is altered by the RF fields generated by nearby conductors. The proper understanding and prediction of how resonators will perform require a model of the current densities flowing in conducting sections, including all RF eddy current effects. Very few models of this type have been presented in the literature. This article presents an overview of one such model and of how it may be applied to a variety of resonators, both shielded and unshielded, circular, and elliptical, in cross section. Results are presented from a shielded head coil operating at 2 tesla. (C) 1997 John Wiley & Sons, Inc.

Topological charge and angular momentum of light beams carrying optical vortices

We analyze the properties of light beams carrying phase singularities, or optical vortices. The transformations of topological charge during free-space propagation of a light wave, which is a combination of a Gaussian beam and a multiple charged optical vortex within a Gaussian envelope, are studied both in theory and experiment. We revise the existing knowledge about topological charge conservation, and demonstrate possible scenarios where additional vortices appear or annihilate during free propagation of such a combined beam. Coaxial interference of optical vortices is also analyzed, and the general rule for angular-momentum density distribution in a combined beam is established. We show that, in spite of any variation in the number of vortices in a combined beam, the total angular momentum is constant during the propagation. [S1050-2947(97)09910-1].

Quantum nonlinear dynamics of continuously measured systems

Classical dynamics is formulated as a Hamiltonian flow in phase space, while quantum mechanics is formulated as unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and classical nonlinear dynamics. Previous solutions have focused on computing quantities associated with a statistical ensemble such as variance or entropy. However a more diner comparison would compare classical predictions to the quantum predictions for continuous simultaneous measurement of position and momentum of a single system, in this paper we give a theory of such measurement and show that chaotic behavior in classical systems fan be reproduced by continuously measured quantum systems.

An ESR study of the gamma radiolysis of aromatic polyesters containing isomeric naphthalene links

Six polyesters were synthesised from 4,4 ' -oxy-bis(benzoyl chloride) and 1,4-, 1,5-, 1,6-, 2,3-, 2,6-, and 2,7-naphthalenediol isomers. The structures of the polyesters were characterised by means of IR, inherent viscosities in tetrachloroethane (TCE), solutions at 303 K and thermal analysis. The glass transition temperatures were in the range of 425-494 K by DSC thermal analysis. All of the polyesters were irradiated in an AECL Gammacell 220 unit at a dose rate of approximately 6.7 kGy/h to doses in the range of 0-15 kGy at 77 and 300 K. ESR spectroscopy was used to examine the radicals formed during radiolysis and to measure their yields. The G-values for radical formation in the polyesters were found to be in the range 0.18-1.41 at 77 K and 0.19-0.78 at 300 K. At 77 K, up to 15% of the radicals formed on radiolysis were found to be photo-bleachable anion radicals. Annealing experiments were carried out in order to identify the neutral radicals, which were assigned to naphthyl- or phenyl- and phenoxyl-type radicals. (C) 2001 Elsevier Science Ltd. All rights reserved.

The use of F-19 NMR for new structure determination in the radiolysis of FEP

The radiation chemistry of poly(tetrafluoroethylene-co-perfluoropropylene), FEP, with a mole fraction of tetrafluoroethylene, TFE, of 0.90 has been studied under vacuum using Co-60 gamma -radiation over absorbed dose ranges up to 3.0 MGy. The radiolysis temperatures were 300, 363, 423 and 523 K. New structure formation in the copolymers was analyzed by solid-state F-19 NMR. The new structures formed in the copolymers have been identified and the G-values for the formation of new -CF3 groups was 2.2 at the lower temperatures and increased to 2.9 at 523 K. The G-value for the loss of original -CF3 groups was approximate to1.0 at all temperatures. At the lower temperatures there was a net loss of -CF-groups on irradiation, G(CF) of -1.3, -0.9 and -0.5 at 300, 363 and 423 K, respectively, but at 523 K there was a net gain with G(CF) equal to 0.8. (C) 2001 Elsevier Science B.V. All rights reserved.

An ESR study on gamma-irradiated poly(vinyl alcohol)

The formation of radicals in poly(vinyl alcohol), PVA, powder irradiated at 77 K by gamma -rays and the transformations of these radicals during photolysis with visible wavelengths and on thermal annealing have been studied. After irradiation a four-line ESR spectrum was observed. It was assigned to a triplet of the C-alpha-radical (38%), with a splitting of 3.27 mT, superimposed on a doublet (62%) with a splitting of 2.7 mT. The doublet appears to be composed of two radicals, one of which is photo-bleachable (58%) and the other which is not photo-bleachable (42%). This suggests that the latter radical is a neutral radical. The photo-bleachable component of the doublet has been assigned to a carbonyl anion radical. but the second doublet due to a neutral radical is unassigned. The total G-value for formation of radicals at 77 K was found to be 2.41 +/- 0.03. Upon illumination with visible light, the anion radicals were removed and the doublet components or the spectrum diminished in intensity, while the three-line spectrum of the C-alpha-radical became more clearly visible. This transition was due to the photo-detachment of electrons from traps which were proposed to be located on carbonyl groups in the polymer resulting from incomplete hydrolysis of the vinyl acetate. The photo-decay of the anion radicals could be satisfactorily described by a two-stage process. The first stage comprised the decay of approximately 80% of the anion radicals present, while the second stage was associated with the decay of the remaining 20%. Subsequent thermal annealing of a photolysed sample to 290 K led to a change in the shape of the spectrum to form a more clearly defined triplet, As the doublet of the neutral radical decays on thermal annealing between 150 and 250K, the C-alpha-radical is formed. (C) 2001 Elsevier Science Ltd. All rights reserved.

A comparative study of the radiation resistance of four optically transparent polyimides

A comparative study of the high energy radiation resistance to formation of radicals in two pairs of polymers is reported. In one pair of polymers the phenyl groups containing the imide rings are separated by an ether linkage and in the other pair they are separated by an hexafluoroisopropylidine group. Two of the polymers contained aromatic amine units linked through an ether linkage and the other two polymers contained a trifluoromethyl biphenyl diamine. The polymers were shown to retain a high level of transparency in the visible region following radiolysis to doses as high as 8 Gy. ESR studies of the resistance to radical formation on radiolysis. at 77 K revealed that the polymers containing ether linkages were more stable than their fluorinated analogues, but all were less stable than Kapton (R). (C) 2001 Elsevier Science Ltd. All rights reserved.

An ESR study of irradiated poly(tetrafluoroethylene-co-perfluoropropyl vinyl ether) (PFA)

Poly(tetrafluoroethylene-co-perfluoropropyl vinyl ether) (PFA) with 2 mol% perfluoropropyl vinyl ether (PPVE) was exposed to gamma -irradiation in vacuum at both 77 K and room temperature and the ESR spectra recorded. Both the main chain, similar to CF2-(CF)-F-.-CF(2)similar to, and end chain, similar to (CF2CF2)-F-. radicals were identified at both temperatures and their thermal stabilities measured, No radicals unique to the radiolytic cleavage at the PPVE units were observed at room temperature, either due to the low concentration of the comonomer or beta -scission to form a chain end radical and a nonradical species. G-values for radical formation at room temperature and 77 K were found to be 0.93 and 0.16, respectively. (C) 2001 Elsevier Science Ltd. All rights reserved.

The use of NMR for determination of new structures in irradiated TFE/PMVE fluoropolymers

The radiation chemistry of two TFE/PMVE copolymers with TFE mole fractions of 0.66 and 0.81 has been studied under vacuum using Co-60 gamma -radiation over absorbed dose ranges up to 4.2 MGy. The radiolysis temperature was 313 K for both TFE/PMVE copolymers. New structure formation in the copolymers was identified by solid-state F-19 NMR and the G-values for new chain ends of 2.1 and 0.5 and for branching sites of 0.9 and 0.2 have been obtained for the TFE/PMVE with TFE mole fractions of 0.66 and 0.81, respectively. The relative yields of-O-CF3 and -CF2-CF3 chain ends were found to be proportional to the copolymer composition, but the yields of the -CF2-CF3 chain ends and -CF- branch points mere not linearly related ia the composition. rather they wets correlated with the radical yields measured at 77 K. (C) 2001 Elsevier Science Ltd. All rights reserved.

Causal and localizable quantum operations

We examine constraints on quantum operations imposed by relativistic causality. A bipartite superoperator is said to be localizable if it can be implemented by two parties (Alice and Bob) who share entanglement but do not communicate, it is causal if the superoperator does not convey information from Alice to Bob or from Bob to Alice. We characterize the general structure of causal complete-measurement superoperators, and exhibit examples that are causal but not localizable. We construct another class of causal bipartite superoperators that are not localizable by invoking bounds on the strength of correlations among the parts of a quantum system. A bipartite superoperator is said to be semilocalizable if it can be implemented with one-way quantum communication from Alice to Bob, and it is semicausal if it conveys no information from Bob to Alice. We show that all semicausal complete-measurement superoperators are semi localizable, and we establish a general criterion for semicausality. In the multipartite case, we observe that a measurement superoperator that projects onto the eigenspaces of a stabilizer code is localizable.

Characterizing mixing and measurement in quantum mechanics

What fundamental constraints characterize the relationship between a mixture rho = Sigma (i)p(i)rho (i) of quantum states, the states rho (i) being mixed, and the probabilities p(i)? What fundamental constraints characterize the relationship between prior and posterior states in a quantum measurement? In this paper we show that then are many surprisingly strong constraints on these mixing and measurement processes that can be expressed simply in terms of the eigenvalues of the quantum states involved. These constraints capture in a succinct fashion what it means to say that a quantum measurement acquires information about the system being measured, and considerably simplify the proofs of many results about entanglement transformation.

Generation of eigenstates using the phase-estimation algorithm

The phase estimation algorithm is so named because it allows an estimation of the eigenvalues associated with an operator. However, it has been proposed that the algorithm can also be used to generate eigenstates. Here we extend this proposal for small quantum systems, identifying the conditions under which the phase-estimation algorithm can successfully generate eigenstates. We then propose an implementation scheme based on an ion trap quantum computer. This scheme allows us to illustrate two simple examples, one in which the algorithm effectively generates eigenstates, and one in which it does not.

Theory of a mode-locked atom laser with toroidal geometry

We consider a possible technique for mode locking an atom laser, based on the generation of a dark soliton in a ring-shaped Bose-Einstein condensate, with repulsive atomic interactions. The soliton is a kink, with angular momentum per particle equal to (h) over bar /2. It emerges naturally when the condensate is stirred at the soliton velocity and cleansed with a periodic out coupler. The result is a replicating coherent field inside the atom laser, stabilized by topology. We give a numerical demonstration of the generation and stabilization of the soliton.

A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function

We compare the performance of two different low-storage filter diagonalisation (LSFD) strategies in the calculation of complex resonance energies of the HO2, radical. The first is carried out within a complex-symmetric Lanczos subspace representation [H. Zhang, S.C. Smith, Phys. Chem. Chem. Phys. 3 (2001) 2281]. The second involves harmonic inversion of a real autocorrelation function obtained via a damped Chebychev recursion [V.A. Mandelshtam, H.S. Taylor, J. Chem. Phys. 107 (1997) 6756]. We find that while the Chebychev approach has the advantage of utilizing real algebra in the time-consuming process of generating the vector recursion, the Lanczos, method (using complex vectors) requires fewer iterations, especially for low-energy part of the spectrum. The overall efficiency in calculating resonances for these two methods is comparable for this challenging system. (C) 2001 Elsevier Science B.V. All rights reserved.

Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.