4,734 research outputs found
Beyond conventional factorization: Non-Hermitian Hamiltonians with radial oscillator spectrum
The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is
revisited in the context of canonical raising and lowering operators. The
Hamiltonian is then factorized in terms of two not mutually adjoint factorizing
operators which, in turn, give rise to a non-Hermitian radial Hamiltonian. The
set of eigenvalues of this new Hamiltonian is exactly the same as the energy
spectrum of the radial oscillator and the new square-integrable eigenfunctions
are complex Darboux-deformations of the associated Laguerre polynomials.Comment: 13 pages, 7 figure
Robustness of the European power grids under intentional attack
The power grid defines one of the most important technological networks of
our times and sustains our complex society. It has evolved for more than a
century into an extremely huge and seemingly robust and well understood system.
But it becomes extremely fragile as well, when unexpected, usually minimal,
failures turn into unknown dynamical behaviours leading, for example, to sudden
and massive blackouts. Here we explore the fragility of the European power grid
under the effect of selective node removal. A mean field analysis of fragility
against attacks is presented together with the observed patterns. Deviations
from the theoretical conditions for network percolation (and fragmentation)
under attacks are analysed and correlated with non topological reliability
measures.Comment: 7 pages, 4 figure
Using Biotic Interaction Networks for Prediction in Biodiversity and Emerging Diseases
Networks offer a powerful tool for understanding and visualizing inter-species interactions within an ecology. Previously considered examples, such as trophic networks, are just representations of experimentally observed direct interactions. However, species interactions are so rich and complex it is not feasible to directly observe more than a small fraction. In this paper, using data mining techniques, we show how potential interactions can be inferred from geographic data, rather than by direct observation. An important application area for such a methodology is that of emerging diseases, where, often, little is known about inter-species interactions, such as between vectors and reservoirs. Here, we show how using geographic data, biotic interaction networks that model statistical dependencies between species distributions can be used to infer and understand inter-species interactions. Furthermore, we show how such networks can be used to build prediction models. For example, for predicting the most important reservoirs of a disease, or the degree of disease risk associated with a geographical area. We illustrate the general methodology by considering an important emerging disease - Leishmaniasis. This data mining approach allows for the use of geographic data to construct inferential biotic interaction networks which can then be used to build prediction models with a wide range of applications in ecology, biodiversity and emerging diseases
Exactly Solvable Hydrogen-like Potentials and Factorization Method
A set of factorization energies is introduced, giving rise to a
generalization of the Schr\"{o}dinger (or Infeld and Hull) factorization for
the radial hydrogen-like Hamiltonian. An algebraic intertwining technique
involving such factorization energies leads to derive -parametric families
of potentials in general almost-isospectral to the hydrogen-like radial
Hamiltonians. The construction of SUSY partner Hamiltonians with ground state
energies greater than the corresponding ground state energy of the initial
Hamiltonian is also explicitly performed.Comment: LaTex file, 21 pages, 2 PostScript figures and some references added.
To be published in J. Phys. A: Math. Gen. (1998
Extended WKB method, resonances and supersymmetric radial barriers
Semiclassical approximations are implemented in the calculation of position
and width of low energy resonances for radial barriers. The numerical
integrations are delimited by t/T<<8, with t the period of a classical particle
in the barrier trap and T the resonance lifetime. These energies are used in
the construction of `haired' short range potentials as the supersymmetric
partners of a given radial barrier. The new potentials could be useful in the
study of the transient phenomena which give rise to the Moshinsky's diffraction
in time.Comment: 12 pages, 4 figures, 3 table
Grothendieck bialgebras, Partition lattices, and symmetric functions in noncommutative variables
We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative variables. In particular this isomorphism singles out a canonical new basis of the symmetric functions in noncommutative variables which would be an analogue of the Schur function basis for this bialgebra
Near ω-continuous multifunctions on bitopological spaces
In this paper, we introduce and study basic characterizations, several properties of upper (lower) nearly (i; j)-!-continuous multifunctions on bitopological space
On real valued ω-continuous functions
The aim of this paper is to introduce and study upper and
lower !-continuous functions. Some characterizations and several proper-
ties concerning upper (resp. lower) !-continuous functions are obtained
Optical potentials using resonance states in Supersymmetric Quantum Mechanics
Complex potentials are constructed as Darboux-deformations of short range,
radial nonsingular potentials. They behave as optical devices which both
refracts and absorbs light waves. The deformation preserves the initial
spectrum of energies and it is implemented by means of a Gamow-Siegert function
(resonance state). As straightforward example, the method is applied to the
radial square well. Analytical derivations of the involved resonances show that
they are `quantized' while the corresponding wave-functions are shown to behave
as bounded states under the broken of parity symmetry of the related
one-dimensional problem.Comment: 16 pages, 6 figures, 1 tabl
Quantum mechanical spectral engineering by scaling intertwining
Using the concept of spectral engineering we explore the possibilities of
building potentials with prescribed spectra offered by a modified intertwining
technique involving operators which are the product of a standard first-order
intertwiner and a unitary scaling. In the same context we study the iterations
of such transformations finding that the scaling intertwining provides a
different and richer mechanism in designing quantum spectra with respect to
that given by the standard intertwiningComment: 8 twocolumn pages, 5 figure
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