3,939 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
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
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
A Hamiltonian functional for the linearized Einstein vacuum field equations
By considering the Einstein vacuum field equations linearized about the
Minkowski metric, the evolution equations for the gauge-invariant quantities
characterizing the gravitational field are written in a Hamiltonian form by
using a conserved functional as Hamiltonian; this Hamiltonian is not the analog
of the energy of the field. A Poisson bracket between functionals of the field,
compatible with the constraints satisfied by the field variables, is obtained.
The generator of spatial translations associated with such bracket is also
obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie
The supersymmetric modified Poschl-Teller and delta-well potentials
New supersymmetric partners of the modified Poschl-Teller and the Dirac's
delta well potentials are constructed in closed form. The resulting
one-parametric potentials are shown to be interrelated by a limiting process.
The range of values of the parameters for which these potentials are free of
singularities is exactly determined. The construction of higher order
supersymmetric partner potentials is also investigated.Comment: 20 pages, LaTeX file, 4 eps figure
Anatomy and tectonic significance of WNW-ESE and NE-SW lineaments at a transpressive plate boundary (Nubia-Iberia)
Recent mapping of the Gulf of Cadiz seafloor permitted to identify major tectonic lineaments: the SWIM lineaments (Zitellini et al., 2009) and Cadiz lineament, striking WNW-ESE and NE-SW, respectively. Multibeam swath bathymetry and interpretation of multi-channel seismic data indicate that these features can be interpreted to correspond to the seafloor morphological expression of active dextral strike-slip faults. Based on the interpreted data and recently published GPS plate kinematic velocity vectors of Nubia with respect to Iberia and the Alboran block (e.g. Fernandes et al.; 2003 Stich et al., 2006) we propose that the SWIM Faults are related to the general NW-SE convergence of Nubia with respect to Iberia, and the Cadiz fault is related to the westward movement of the Gibraltar orogenic arc
Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra
It is shown that the radial part of the Hydrogen Hamiltonian factorizes as
the product of two not mutually adjoint first order differential operators plus
a complex constant epsilon. The 1-susy approach is used to construct
non-hermitian Hamiltonians with hydrogen spectra. Other non-hermitian
Hamiltonians are shown to admit an extra `complex energy' at epsilon. New
self-adjoint hydrogen-like Hamiltonians are also derived by using a 2-susy
transformation with complex conjugate pairs epsilon, (c.c) epsilon.Comment: LaTeX2e file, 13 pages, 6 EPS figures. New references added. The
present is a reorganized and simplified versio
- …