Probability backflow for a Dirac particle

The phenomenon of probability backflow, previously quantified for a free nonrelativistic particle, is considered for a free particle obeying Dirac's equation. It is known that probability backflow can occur in the opposite direction to the momentum; that is to say, there exist positive-energy states in which the particle certainly has a positive momentum in a given direction, but for which the component of the probability flux vector in that direction is negative. It is shown thar the maximum possible amount of probability that can flow backwards, over a given time interval of duration T, depends on the dimensionless parameter epsilon = root 4h/mc(2)T, where m is the mass of the particle and c is the speed of light. At epsilon = 0, the nonrelativistic value of approximately 0.039 for this maximum is recovered. Numerical studies suggest that the maximum decreases monotonically as epsilon increases from 0, and show that it depends on the size of m, h, and T, unlike the nonrelativistic case.

The velocity of probability transport in quantum mechanics

In his study of the 'time of arrival' problem in the nonrelativistic quantum mechanics of a single particle, Allcock [1] noted that the direction of the probability flux vector is not necessarily the same as that of the mean momentum of a wave packet, even when the packet is composed entirely of plane waves with a common direction of momentum. Packets can be constructed, for example for a particle moving under a constant force, in which probability flows for a finite time in the opposite direction to the momentum. A similar phenomenon occurs for the Dirac electron. The maximum amount of probabilitiy backflow which can occur over a given time interval can be calculated in each case.

Localizing the relativistic electron

A causally well-behaved solution of the localization problem for the free electron is given, with natural space-time transformation properties, in terms of Dirac's position operator x. It is shown that, although x is not an observable in the usual sense, and has no positive-energy (generalized) eigenstates, the four-vector density (rho(x, t), j(x, t)/c) is observable, and can be localized arbitrarily precisely about any point in space, at any instant of time, using only positive energy states. A suitable spin operator can be diagonalized at the same time.

Bounds on integrals of the Wigner function

The integral of the Wigner function over a subregion of the phase space of a quantum system may be less than zero or greater than one. It is shown that for systems with 1 degree of freedom, the problem of determining the best possible upper and lower bounds on such an integral, over an possible states, reduces to the problem of finding the greatest and least eigenvalues of a Hermitian operator corresponding to the subregion. The problem is solved exactly in the case of an arbitrary elliptical region. These bounds provide checks on experimentally measured quasiprobability distributions.

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Semiquantum versus semiclassical mechanics for simple nonlinear systems

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behavior of expectation values of simple observables and of eigenvalues of the Groenewold operator are calculated numerically and compared for the various semiclassical and semiquantum approximations.

Evaluation of fly ash as a component of potting substrates

A series of laboratory and glasshouse experiments were undertaken to assess the potential for incorporation of fly ash in soilless potting substrates. The physical and chemical properties of a commercially available bark based substrate, the University of California (UC) 1:1 peat:sand mix and a range uf test substrates containing fly ash were characterised. In test mixtures, fly ash was substituted for a portion of either the peat or sand component of the UC mix, at rates of 10, 20, 30 and 50% of the mix volume, Incorporation of fly ash greatly increased the plant available water capacity (10-1500 kPa) of the substrate. However, high pH, increased substrate strength and reduced air-filled porosity were considered adverse effects, particularly at ash rates > 20%. The growth of tomato (Lycopersicon esculentum), petunia (Petunia x hybrida grandiflora) and Boston fern (Nephrolepis exaltata) in the substrates was assessed. Two watering regimes, capillary watering and irregular hosing, were used to identify effects of available water capacity on plant growth, but no effect was identified. Test mixtures containing fly ash as 20% of the substrate volume produced growth equal to that in the UC mix, with substrates containing 10% ash producing significantly greater growth of tomato and petunia. At rates of incorporation > 20% reduced plant growth was attributed to both adverse physical and chemical characteristics of the substrate. As fly ash is available at low cost and can be successfully substituted for a considerable portion of the expensive peat component, its use at low application rates in potting substrates may be desirable from an economic viewpoint.

Interconnected-tubes model of hepatic elimination

The distributed-tubes model of hepatic elimination is extended to include intermixing between sinusoids, resulting in the formulation of a new, interconnected-tubes model. The new model is analysed for the simple case of two interconnected tubes, where an exact solution is obtained. For the case of many strongly-interconnected tubes, it is shown that a zeroth-order approximation leads to the convection-dispersion model. As a consequence the dispersion number is expressed, for the first time, in terms of its main physiological determinants: heterogeneity of flow and density of interconnections between sinusoids. The analysis of multiple indicator dilution data from a perfused liver preparation using the simplest version of the model yields the estimate 10.3 for the average number of interconnections. The problem of boundary conditions for the dispersion model is considered from the viewpoint that the dispersion-convection equation is a zeroth-order approximation to the equations for the interconnected-tubes model. (C) 1997 Academic Press Limited.

Casimir invariants and characteristic identities for gl(infinity)

A full set of (higher-order) Casimir invariants for the Lie algebra gl(infinity) is constructed and shown to be well defined in the category O-FS generated by the highest weight (unitarizable) irreducible representations with only a finite number of nonzero weight components. Moreover, the eigenvalues of these Casimir invariants are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(infinity) are also determined and generalize those previously obtained for gl(n) by Bracken and Green [A. J. Bracken and H. S. Green, J. Math. Phys. 12, 2099 (1971); H. S. Green, ibid. 12, 2106 (1971)]. (C) 1997 American Institute of Physics.

Algebraic Bethe ansatz for integrable extended Hubbard models arising from supersymmetric group solutions

Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded quantum inverse scattering method. The Bethe ansatz equations for all these models are derived by using the algebraic Bethe ansatz method.

Integrable extended hubbard models with boundary Kondo impurities

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.

The development of a pilot telemedicine network in Scotland: lessons learned

A pilot telemedicine network was established in 11 sites using funding provided by the Department of Trade and Industry in the UK. The main purpose of the project was to develop and evaluate clinical and educational links between central and peripheral sites in Scotland, The results were very encouraging, and clinical services were established in accident and emergency medicine, tele-ultrasound and clinical psychology. An undergraduate medical teaching service was also successfully established. All of these services are to be continued after the completion of the project. Many lessons were learned during the establishment of this network which will be useful in future projects. These included the importance of training for telemedicine users, the importance of identifying a telemedicine champion, the pitfall of health economics and the fact that services must be needs driven.

Promoters for pregenomic RNA of banana streak badnavirus are active for transgene expression in monocot and dicot plants

Two putative promoters from Australian banana streak badnavirus (BSV) isolates were analysed for activity in different plant species. In transient expression systems the My (2105 bp) and Cv (1322 bp) fragments were both shown to have promoter activity in a wide range of plant species including monocots (maize, barley, banana, millet, wheat, sorghum), dicots (tobacco, canola, sunflower, Nicotiana benthamiana, tipu tree), gymnosperm (Pinus radiata) and fern (Nephrolepis cordifolia). Evaluation of the My and Cv promoters in transgenic sugarcane, banana and tobacco plants demonstrated that these promoters could drive high-level expression of either the green fluorescent protein (GFP) or the beta -glucuronidase (GUS) reporter gene (uidA) in vegetative plant cells. In transgenic sugarcane plants harbouring the Cv promoter, GFP expression levels were comparable or higher (up to 1.06% of total soluble leaf protein as GFP) than those of plants containing the maize ubiquitin promoter (up to 0.34% of total soluble leaf protein). GUS activities in transgenic in vitro-grown banana plants containing the My promoter were up to seven-fold stronger in leaf tissue and up to four-fold stronger in root and corm tissue than in plants harbouring the maize ubiquitin promoter. The Cv promoter showed activities that were similar to the maize ubiquitin promoter in in vitro-grown banana plants, but was significantly reduced in larger glasshouse-grown plants. In transgenic in vitro-grown tobacco plants, the My promoter reached activities close to those of the 35S promoter of cauliflower mosaic virus (CaMV), while the Cv promoter was about half as active as the CaMV 35S promoter. The BSV promoters for pregenomic RNA represent useful tools for the high-level expression of foreign genes in transgenic monocots.

Catheter effects in organ perfusion experiments

In a typical isolated organ perfusion experiment, a substance is injected upstream of an organ and then collected at some distance downstream. To reach the organ from the injection site, and then from the organ to the collector, a solute passes through catheters, usually tubes with circular cross-sections. Catheters cause distortion to the concentration-time profile of the perfusion. In this paper, we analyse catheter distribution kinetics from a mathematical point of view, develop the function most suitable for modeling this distribution and successfully apply this function to experimental data. (C) 2002 Academic Press.