Measurement of qubits

We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (qubits). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of entangled photons generated in a down-conversion experiment; however, the discussion applies in general, regardless of the actual physical realization. Two techniques are discussed, namely, a tomographic reconstruction (in which the density matrix is linearly related to a set of measured quantities) and a maximum likelihood technique which requires numerical optimization (but has the advantage of producing density matrices that are always non-negative definite). In addition, a detailed error analysis is presented, allowing errors in quantities derived from the density matrix, such as the entropy or entanglement of formation, to be estimated. Examples based on down-conversion experiments are used to illustrate our results.

A flexible method for rapid force computation in elliptical magnets

The design of open-access elliptical cross-section magnet systems has recently come under consideration. Obtaining values for the forces generated within these unusual magnets is important to progress the designs towards feasible instruments. This paper presents a novel and flexible method for the rapid computation of forces within elliptical magnets. The method is demonstrated by the analysis of a clinical magnetic resonance imaging magnet of elliptical cross-section and open design. The analysis reveals the non-symmetric nature of the generated Maxwell forces, which are an important consideration, particularly in the design of superconducting systems.

An inverse design method for elliptical MRI magnets

An inverse, current density mapping (CDM) method has been developed for the design of elliptical cross-section MRI magnets. The method provides a rapid prototyping system for unusual magnet designs, as it generates a 3D current density in response to a set of target field and geometric constraints. The emphasis of this work is on the investigation of new elliptical coil structures for clinical MRI magnets. The effect of the elliptical aspect ratio on magnet performance is investigated. Viable designs are generated for symmetric, asymmetric and open architecture elliptical magnets using the new method. Clinically relevant attributes such as reduced stray field and large homogeneous regions relative to total magnet length are included in the design process and investigated in detail. The preliminary magnet designs have several novel features.

Compact clinical MRI magnet design using a multilayer current density approach

In this work, a new method of optimization is successfully applied to the theoretical design of compact, actively shielded, clinical MRI magnets. The problem is formulated as a two-step process in which the desired current densities on multiple, cc-axial surface layers are first calculated by solving Fredholm equations of the first kind. Non-linear optimization methods with inequality constraints are then invoked to fit practical magnet coils to the desired current densities. The current density approach allows rapid prototyping of unusual magnet designs. The emphasis of this work is on the optimal design of short, actively-shielded MRI magnets for whole-body imaging. Details of the hybrid numerical model are presented, and the model is used to investigate compact, symmetric, and asymmetric MRI magnets. Magnet designs are presented for actively-shielded, symmetric magnets of coil length 1.0 m, which is considerably shorter than currently available designs of comparable dsv size. Novel, actively-shielded, asymmetric magnet designs are also presented in which the beginning of a 50-cm dsv is positioned just 11 cm from the end of the coil structure, allowing much improved access to the patient and reduced patient claustrophobia. Magn Reson Med 45:331540, 2001. (C) 2001 Wiley-Liss, Inc.

Quantification of sulfur and sulfur-containing compounds in wastewaters by means of a combination of liquid chromatographic methods

Low-micromolar concentrations of sulfite, thiosulfate and sulfide, present in synthetic wastewater or anaerobic digester effluent, were quantified by means of derivatization with monobromobimane, followed by HPLC separation with fluorescence detection. The concentration of elemental sulfur was determined, after its extraction with chloroform from the derivatized sample, by HPLC with UV detection. Recoveries of sulfide (both matrices), and of thiosulfate and sulfite (synthetic wastewater) were between 98 and 103%. The in-run RSDs on separate derivatizations were 13 and 19% for sulfite (two tests), between 1.5 and 6.6% for thiosulfate (two tests) and between 4.1 and 7.7% for sulfide (three tests). Response factors for derivatives of sulfide and thiosulfate, but not sulfite, were steady over a 13-month period during which 730 samples were analysed. Dithionate and tetrathionate did not seem to be detectable with this method. The distinctness of the elemental sulfur and the derivatizing-agent peaks was improved considerably by detecting elution at 297 instead of 263 nm. (C) 2002 Elsevier Science B.V. All rights reserved.

Brief note on the variation of constants formula for fuzzy differential equations

This note gives a theory of state transition matrices for linear systems of fuzzy differential equations. This is used to give a fuzzy version of the classical variation of constants formula. A simple example of a time-independent control system is used to illustrate the methods. While similar problems to the crisp case arise for time-dependent systems, in time-independent cases the calculations are elementary solutions of eigenvalue-eigenvector problems. In particular, for nonnegative or nonpositive matrices, the problems at each level set, can easily be solved in MATLAB to give the level sets of the fuzzy solution. (C) 2002 Elsevier Science B.V. All rights reserved.

Integrability and exact spectrum of a pairing model for nucleons

A pairing model for nucleons, introduced by Richardson in 1966, which describes proton-neutron pairing as well as proton-proton and neutron-neutron pairing, is re-examined in the context of the quantum inverse scattering method. Specifically, this shows that the model is integrable by enabling the explicit construction of the conserved operators. We determine the eigenvalues of these operators in terms of the Bethe ansatz, which in turn leads to an expression for the energy eigenvalues of the Hamiltonian.

Current density mapping approach for design of clinical magnetic resonance imaging magnets

Novel current density mapping (CDM) schemes are developed for the design of new actively shielded, clinical magnetic resonance imaging (MRI) magnets. This is an extended inverse method in which the entire potential solution space for the superconductors has been considered, rather than single current density layers. The solution provides an insight into the required superconducting coil pattern for a desired magnet configuration. This information is then used as an initial set of parameters for the magnet structure, and a previously developed hybrid numerical optimization technique is used to obtain the final geometry of the magnet. The CDM scheme is applied to the design of compact symmetric, asymmetric, and open architecture 1.0-1.5 T MRI magnet systems of novel geometry and utility. A new symmetric 1.0-T system that is just I m in length with a full 50-cm diameter of the active, or sensitive, volume (DSV) is detailed, as well as an asymmetric system in which a 50-cm DSV begins just 14 cm from the end of the coil structure. Finally a 1.0-T open magnet system with a full 50-cm DSV is presented. These new designs provide clinically useful homogeneous regions and have appropriately restricted stray fields but, in some of the designs, the DSV is much closer to the end of the magnet system than in conventional designs. These new designs have the potential to reduce patient claustrophobia and improve physician access to patients undergoing scans. (C) 2002 Wiley Periodicals, Inc.

Carbene and nitrene rearrangements: A theoretical study of cyclic allenes and carbenes, carbodiimides, and azirines

B3LYP/6-31G(d) calculations of structures, energies, and infrared spectra of several rearrangement products of (hetero)aromatic nitrenes and carbenes are reported. 3-Isoquinolylnitrene 36 ring closes to the azirine 37 prior to ring expansion to the potentially stable but unobserved seven-membered-ring carbodiimide 38 and diazacycloheptatrienylidene C-s-39S. A new, stable cycloheptatrienylidene, C-s-19S, is located on the naphthylcarbene energy surface. 4-Quinolylnitrene undergoes reaction via the azirine 50 in solution, but ring expansion to the stable seven-membered-ring ketenimine 47 under Ar matrix photolysis conditions. There is excellent agreement between calculated infrared spectra of 1,5-diazacyclohepta-1,2,4,6-tetraene 54 (obtained by photolysis of 4-pyridyl azide), 1-azacyclohepta-1,2,4,6-tetraene 5, 1-azacyclohepta-1,3,5,6-tetraene 55, and 1-azacyclohepta-1,3,4,6-tetraene 56 and the available experimental data.

Quinolizine-2,4-diones by reversible dimerisation 2-pyridylketenes

Quinolizine-2,4-diones 11 are obtained by ash vacuum thermolysis (FVT) of 3-acyl-1,2,3-triazolo[1,5-a]pyridines 7. The reaction takes place via methyl- and phenyl(2-pyridyl)ketenes 10, which are directly observable by infrared spectroscopy in low temperature matrices. FVT of 11 regenerates the ketenes 10.

Chemistry of stable iminopropadienones, RN=C=C=C=O

The synthesis, spectroscopic properties, and chemical reactions of the stable (neopentylimino)-, (mesitylimino)-, and (o-tert-butylphenylimino)propadienones (6) are reported. Nucleophilic addition of amines affords the malonic amidoamidines 7 and 8. 3,5-Dimethylpyrazole reacts analogously to form 9b. Addition of 1,2-dimethylhydrazine produces pyrazolinones 10-12. Addition of N,Y'-dimethyldiaminoethane, -propane, and -butane gives diazepine, diazocine, and diazonine derivatives 13-15, respectively (X-ray structures of 13c, 14a, and 15a are available). The mesoionic pyridopyrimidinium olates IS are obtained by addition of 2-(methylamino)pyridine (X-ray structure of 18b available). Primary 2-aminopyridines afford the pyridopyrimidininones 20-29 and 31 (X-ray structure of 21a available), and 2-aminopyrimidines and 2-aminopyrazine afford pyrimidopyrimidinones and pyrazinopyrimidinones 33-35. Pyrimidoisoquinolinone 36 results from 1-aminoisoquinoline and pyridoquinolinone 40 from 8-aminoquinoline. 2-Aminothiazoline and 2-aminothiazole afford thiazolopyrimidinone derivatives 41-43 (X-ray structure of 43a available).

From molecular complexes to zwitterions and final products. Reactions between C3O2 and amines

The formation of molecular complexes (prereactive intermediates) between C3O2 and amines (ammonia, dimethylamine, trimethylamine, and 4-(dimethylamino)pyridine) as well as the subsequent transformation of the complexes into C3O2-amine zwitterions in cryogenic matrixes (ca. 40 K) has been observed. In the case of dimethylamine, the formation of tetramethylmalonamide has also been documented. Calculations using density functional theory (B3LYP/6-31G(2d, p)) are used to assign all above species and are in excellent agreement with the IR spectra.

Modelling of Lamb waves in composite laminated plates excited by interdigital transducers

The technique of permanently attaching interdigital transducers (IDT) to either flat or curved structural surfaces to excite single Lamb wave mode has demonstrated great potential for quantitative non-destructive evaluation and smart materials design, In this paper, the acoustic wave field in a composite laminated plate excited by an IDT is investigated. On the basis of discrete layer theory and a multiple integral transform method, an analytical-numerical approach is developed to evaluate the surface velocity response of the plate due to the IDTs excitation. In this approach, the frequency spectrum and wave number spectrum of the output of IDT are obtained directly. The corresponding time domain results are calculated by applying a standard inverse fast Fourier transformation technique. Numerical examples are presented to validate the developed method and show the ability of mode selection and isolation. A new effective way of transfer function estimation and interpretation is presented by considering the input wave number spectrum in addition to the commonly used input frequency spectrum. The new approach enables the simple physical evaluation of the influences of IDT geometrical features such as electrode finger widths and overall dimension and excitation signal properties on the input-output characteristics of IDT. Finally, considering the convenience of Mindlin plate wave theory in numerical computations as well as theoretical analysis, the validity is examined of using this approximate theory to design IDT for the excitation of the first and second anti-symmetric Lamb modes. (C) 2002 Elsevier Science Ltd. All rights reserved.

A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.

Application of the maximum entropy method to the (2 + 1)D four-fermion model

We investigate spectral functions extracted using the maximum entropy method from correlators measured in lattice simulations of the (2+1)-dimensional four-fermion model. This model is particularly interesting because it has both a chirally broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are only resonances. In the broken phase we study the elementary fermion, pion, sigma, and massive pseudoscalar meson; our results confirm the Goldstone nature of the π and permit an estimate of the meson binding energy. We have, however, seen no signal of σ→ππ decay as the chiral limit is approached. In the symmetric phase we observe a resonance of nonzero width in qualitative agreement with analytic expectations; in addition the ultraviolet behavior of the spectral functions is consistent with the large nonperturbative anomalous dimension for fermion composite operators expected in this model.