Development of an Extended Product Lifecycle Management through Service Oriented Architecture.

Organised by: Cranfield UniversityThe aim of this work is to define new business opportunities through the concept of Extended Product Lifecycle Management (ExtPLM), analysing its potential implementation within a Service Oriented Architecture. ExtPLM merges the concepts of Extended Product, Avatar and PLM. It aims at allowing a closer interaction between enterprises and their customers, who are integrated in all phases of the life cycle, creating new technical functionalities and services, improving both the practical (e.g. improving usage, improving safety, allowing predictive maintenance) and the emotional side (e.g. extreme customization) of the product.Mori Seiki – The Machine Tool Company; BAE Systems; S4T – Support Service Solutions: Strategy and Transitio

SUSY Quantum Mechanics with Complex Superpotentials and Real Energy Spectra

We extend the standard intertwining relations used in Supersymmetrical (SUSY) Quantum Mechanics which involve real superpotentials to complex superpotentials. This allows to deal with a large class of non-hermitean Hamiltonians and to study in general the isospectrality between complex potentials. In very specific cases we can construct in a natural way "quasi-complex" potentials which we define as complex potentials having a global property such as to lead to a Hamiltonian with real spectrum. We also obtained a class of complex transparent potentials whose Hamiltonian can be intertwined to a free Hamiltonian. We provide a variety of examples both for the radial problem (half axis) and for the standard one-dimensional problem (the whole axis), including remarks concerning scattering problems.Comment: 22 pages, Late

Matrix Hamiltonians: SUSY approach to hidden symmetries

A new supersymmetric approach to the analysis of dynamical symmetries for matrix quantum systems is presented. Contrary to standard one dimensional quantum mechanics where there is no role for an additional symmetry due to nondegeneracy, matrix hamiltonians allow for non-trivial residual symmetries. This approach is based on a generalization of the intertwining relations familiar in SUSY Quantum Mechanics. The corresponding matrix supercharges, of first or of second order in derivatives, lead to an algebra which incorporates an additional block diagonal differential matrix operator (referred to as a "hidden" symmetry operator) found to commute with the superhamiltonian. We discuss some physical interpretations of such dynamical systems in terms of spin 1/2 particle in a magnetic field or in terms of coupled channel problem. Particular attention is paid to the case of transparent matrix potentials.Comment: 20 pages, LaTe

Complex Lagrangians and phantom cosmology

Motivated by the generalization of quantum theory for the case of non-Hermitian Hamiltonians with PT symmetry, we show how a classical cosmological model describes a smooth transition from ordinary dark energy to the phantom one. The model is based on a classical complex Lagrangian of a scalar field. Specific symmetry properties analogous to PT in non-Hermitian quantum mechanics lead to purely real equation of motion.Comment: 11 pages, to be published in J.Phys.A, refs. adde

Reflectionless PT-symmetric potentials in the one-dimensional Dirac equation

We study the one-dimensional Dirac equation with local PT-symmetric potentials whose discrete eigenfunctions and continuum asymptotic eigenfunctions are eigenfunctions of the PT operator, too: on these conditions the bound-state spectra are real and the potentials are reflectionless and conserve unitarity in the scattering process. Absence of reflection makes it meaningful to consider also PT-symmetric potentials that do not vanish asymptotically.Comment: 24 pages, to appear in J. Phys. A : Math. Theor; one acknowledgement and one reference adde

Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution

We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of variables. In the present case, the property of shape invariance provides the equidistant form of the spectrum and the algorithm to construct eigenfunctions analytically. It is shown that the Hamiltonian is non-diagonalizable, and the resolution of identity must include also the corresponding associated functions. In the specific case of anharmonic second-plus-fourth order interaction, expressions for the wave functions and associated functions are constructed explicitly for the lowest levels, and the recursive algorithm to produce higher level wave functions is given.Comment: 17 p.

New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach

New solutions for second-order intertwining relations in two-dimensional SUSY QM are found via the repeated use of the first order supersymmetrical transformations with intermediate constant unitary rotation. Potentials obtained by this method - two-dimensional generalized P\"oschl-Teller potentials - appear to be shape-invariant. The recently proposed method of $SUSY-$separation of variables is implemented to obtain a part of their spectra, including the ground state. Explicit expressions for energy eigenvalues and corresponding normalizable eigenfunctions are given in analytic form. Intertwining relations of higher orders are discussed.Comment: 21 pages. Some typos corrected; imrovements added in Subsect.4.2; some references adde

Higher Order Matrix SUSY Transformations in Two-Dimensional Quantum Mechanics

The iteration procedure of supersymmetric transformations for the two-dimensional Schroedinger operator is implemented by means of the matrix form of factorization in terms of matrix 2x2 supercharges. Two different types of iterations are investigated in detail. The particular case of diagonal initial Hamiltonian is considered, and the existence of solutions is demonstrated. Explicit examples illustrate the construction.Comment: 15