86 research outputs found
Pseudo Memory Effects, Majorization and Entropy in Quantum Random Walks
A quantum random walk on the integers exhibits pseudo memory effects, in that
its probability distribution after N steps is determined by reshuffling the
first N distributions that arise in a classical random walk with the same
initial distribution. In a classical walk, entropy increase can be regarded as
a consequence of the majorization ordering of successive distributions. The
Lorenz curves of successive distributions for a symmetric quantum walk reveal
no majorization ordering in general. Nevertheless, entropy can increase, and
computer experiments show that it does so on average. Varying the stages at
which the quantum coin system is traced out leads to new quantum walks,
including a symmetric walk for which majorization ordering is valid but the
spreading rate exceeds that of the usual symmetric quantum walk.Comment: 3 figures include
Phase-space-region operators and the Wigner function: Geometric constructions and tomography
Quasiprobability measures on a canonical phase space give rise through the action of Weyl's quantization map to operator-valued measures and, in particular, to region operators. Spectral properties, transformations, and general construction methods of such operators are investigated. Geometric trace-increasing maps of density operators are introduced for the construction of region operators associated with one-dimensional domains, as well as with two-dimensional shapes (segments, canonical polygons, lattices, etc.). Operational methods are developed that implement such maps in terms of unitary operations by introducing extensions of the original quantum system with ancillary spaces (qubits). Tomographic methods of reconstruction of the Wigner function based on the radon transform technique are derived by the construction methods for region operators. A Hamiltonian realization of the region operator associated with the radon transform is provided, together with physical interpretations
A New Supersymmetric and Exactly Solvable Model of Correlated Electrons
A new lattice model is presented for correlated electrons on the unrestricted
-dimensional electronic Hilbert space (where
is the lattice length). It is a supersymmetric generalization of the
Hubbard model, but differs from the extended Hubbard model proposed by Essler,
Korepin and Schoutens. The supersymmetry algebra of the new model is
superalgebra . The model contains one symmetry-preserving free real
parameter which is the Hubbard interaction parameter , and has its origin
here in the one-parameter family of inequivalent typical 4-dimensional irreps
of . On a one-dimensional lattice, the model is exactly solvable by
the Bethe ansatz.Comment: 10 pages, LaTex. (final version to appear in Phys.Rev.Lett.
Infinite Families of Gauge-Equivalent -Matrices and Gradations of Quantized Affine Algebras
Associated with the fundamental representation of a quantum algebra such as
or , there exist infinitely many gauge-equivalent
-matrices with different spectral-parameter dependences. It is shown how
these can be obtained by examining the infinitely many possible gradations of
the corresponding quantum affine algebras, such as and
, and explicit formulae are obtained for those two cases.
Spectral-dependent similarity (gauge) transformations relate the -matrices
in different gradations. Nevertheless, the choice of gradation can be
physically significant, as is illustrated in the case of quantum affine Toda
field theories.Comment: 14 pages, Latex, UQMATH-93-10 (final version for publication
Boundary two-parameter eight-state supersymmetric fermion model and Bethe ansatz solution
The recently introduced two-parameter eight-state
supersymmetric fermion model is extended to include boundary terms. Nine
classes of boundary conditions are constructed, all of which are shown to be
integrable via the graded boundary quantum inverse scattering method. The
boundary systems are solved by using the coordinate Bethe ansatz and the Bethe
ansatz equations are given for all nine cases.Comment: 11 pages, RevTex; some typos correcte
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 disks 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
Hilbert space carrying the positive discrete series representations of the
algebra su(1,1)or so(2,1). The explicit relation between the spectra of
operators associated with disks and circles with proportional radii, is given
in terms of the dicrete variable Meixner polynomials.Comment: 11 pages, latex fil
Phase-space-region operators and the Wigner function: Geometric constructions and tomography
Quasiprobability measures on a canonical phase space give rise through the action of Weyl's quantization map to operator-valued measures and, in particular, to region operators. Spectral properties, transformations, and general construction methods of such operators are investigated. Geometric trace-increasing maps of density operators are introduced for the construction of region operators associated with one-dimensional domains, as well as with two-dimensional shapes (segments, canonical polygons, lattices, etc.). Operational methods are developed that implement such maps in terms of unitary operations by introducing extensions of the original quantum system with ancillary spaces (qubits). Tomographic methods of reconstruction of the Wigner function based on the radon transform technique are derived by the construction methods for region operators. A Hamiltonian realization of the region operator associated with the radon transform is provided, together with physical interpretations
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.Comment: 15 pages, RevTex, No figures, to be published in J. Phys.
Development of the Liverpool Adverse Drug Reaction Avoidability Assessment Tool
Aim
To develop and test a new tool to assess the avoidability of adverse drug reactions that is suitable for use in paediatrics but which is also applicable to a variety of other settings.
Methods
The study involved multiple phases. Preliminary work involved using the Hallas scale and a modification of the existing Hallas scale, to assess two different sets of adverse drug reaction (ADR) case reports. Phase 1 defined, modified and refined a new tool using multidisciplinary teams. Phase 2 involved the assessment of 50 ADR case reports from a prospective study of paediatric inpatients by individual assessors. Phase 3 compared assessments with the new tool for individuals and groups in comparison to the ‘gold standard’ (the avoidability outcome set by a panel of senior investigators: an experienced clinical pharmacologist, paediatrician and pharmacist).
Main Outcome Measures
Inter-rater reliability (IRR), measure of disagreement and utilization of avoidability categories.
Results
Preliminary work—Pilot phase: results for the original Hallas cases were fair and pairwise kappa scores ranged from 0.21 to 0.36. Results for the modified Hallas cases were poor, pairwise kappa scores ranged from 0.06 to 0.16.
Phase 1: on initial use of the new tool, agreement between the two multidisciplinary groups was found on 13/20 cases with a kappa score of 0.29 (95% CI -0.04 to 0.62).
Phase 2: the assessment of 50 ADR case reports by six individual reviewers yielded pairwise kappa scores ranging from poor to good 0.12 to 0.75 and percentage exact agreement (%EA) ranged from 52–90%.
Phase 3: Percentage exact agreement ranged from 35–70%. Overall, individuals had better agreement with the ‘gold standard’.
Conclusion
Avoidability assessment is feasible but needs careful attention to methods. The Liverpool ADR avoidability assessment tool showed mixed IRR. We have developed and validated a method for assessing the avoidability of ADRs that is transparent, more objective than previous methods and that can be used by individuals or groups
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