Browsing by Author "Urrutia, L. F."

Now showing 1 - 6 of 6
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    Alternative Approaches to Lorentz Violation Invariance in Loop Quantum Gravity Inspired Models
    (2004) Alfaro Solís, Jorge Luis; Morales-Técotl, Hugo A.; Reyes, Marat; Urrutia, L. F.
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    An SU(2) ⊗ SU(2) Jaynes-Cummings model with a maximum energy level
    (2014) Martin Ruiz, A.; Frank, Alejandro; Urrutia, L. F.
    The SU(2) circle times SU(2) extension of the Jaynes-Cummings model provides a quantum mechanical system with a finite Hilbert space together with a maximum energy level in the spectrum. The model, which remains exactly solvable, is based on the replacement of the bosonic (creation and annihilation) operators by spin operators defined to act within a definite SU(2) irreducible representation, in such a way that the photon field has a finite number of excitations. The usual Heisenberg-Weyl (h(1)) algebra can be obtained by contraction of the su(2) Lie algebra. We analyze the behavior of both the atomic and field quantum properties, like collapse and revivals, photon antibunching and squeezing, giving special attention to their dependence upon the maximum number of photon excitations.
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    Exact solution of the Schrödinger equation for an hydrogen atom at the interface between the vacuum and a topologically insulating surface
    (2019) Bonilla Moreno, Daniel; Martín Ruiz, A.; Urrutia, L. F.
    When an hydrogen atom is brought near to the interface between θ-media, the quantum-mechanical motion of the electron will be affected by the electromagnetic interaction between the atomic charges and the θ-interface, which is described by an axionic extension of Maxwell electrodynamics in the presence of a boundary. In this paper we investigate the atom-surface interaction effects upon the energy levels and wave functions of an hydrogen atom placed at the interface between a θ-medium and the vacuum. In the approximation considered, the Schrödinger equation can be exactly solved by separation of variables in terms of hypergeometic functions for the angular part and hydrogenic functions for the radial part. In order to make such effects apparent we deal with unrealistic high values of the θ-parameter. We also compute the energy shifts using perturbation theory for a particular small value of θ and we demonstrate that they are in a very good agreement with the ones obtained from the exact solution.
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    Invariants of the electromagnetic field
    (2014) Escobar, C. A.; Urrutia, L. F.
    We present a constructive proof that, in electrodynamics, all of the gauge-invariant Lorentz scalars and pseudoscalars can be expressed as functions of the quadratic ones. (C) 2014 AIP Publishing LLC.
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    Quantum Gravity and Spin-1/2 Particle Effective Dynamics
    (2002) Alfaro Solís, Jorge Luis; Morales, H. A.; Urrutia, L. F.
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    The Goldstone theorem in non-linear electrodynamics
    (2014) Escobar, C. A.; Urrutia, L. F.
    We construct a non-linear electrodynamics arising from the spontaneous Lorentz symmetry breaking triggered by a non-zero vacuum expectation value of the electromagnetic field strength, instead of the electromagnetic potential. The expansion of the corresponding action in terms of the physical photon excitations is naturally written in terms of generalized permeabilities, in a manner similar to when the polarization is expanded in terms of the susceptibilities when studying non-linear effects in standard optics. The new version of the Goldstone theorem is investigated and implies that the lowest-order permeability, been the analogous of the mass matrix in the standard case, has zero modes. These are interpreted as the corresponding Goldstone modes of the model and they are explicitly constructed for one of the two choices of vacua that the theory admits. Further iterations of the method employed to obtain such theorem yield relationships among the generalized permeabilities. Some preliminary results regarding the splitting of the two degrees of freedom of the model into Goldstone and non-Goldstone modes are presented. Copyright (C) EPLA, 2014