Papers by Alfonso Jauregui
We show that when an isolated doublet of unbound states of a physical system becomes degenerate f... more We show that when an isolated doublet of unbound states of a physical system becomes degenerate for some values of the control parameters of the system, the energy hypersurfaces representing the complex resonance energy eigenvalues as functions of the control parameters have an algebraic branch point of rank one in parameter space. Associated with this singularity in parameter space, the scattering matrix, S ℓ (E), and the Green's function, G (+) ℓ (k; r, r ′ ), have one double pole in the unphysical sheet of the complex energy plane. We characterize the universal unfolding or deformation of a typical degeneracy point of two unbound states in parameter space by means of a universal 2-parameter family of functions which is contact equivalent to the pole position function of the isolated doublet of resonances at the exceptional point and includes all small perturbations of the degeneracy condition up to contact equivalence.
We solved numerically the implicit, trascendental equation that defines the eigenenergy surface o... more We solved numerically the implicit, trascendental equation that defines the eigenenergy surface of a degenerating isolated doublet of unbound states in the simple but illustrative case of the scattering of a beam of particles by a double barrier potential. Unfolding the degeneracy point with the help of a contact equivalent approximant, crossings and anticrossings of energies and widths, as well as the changes of identity of the poles of the S−matrix are explained in terms of sections of the eigenenergy surfaces.
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Papers by Alfonso Jauregui