A note on the Moll-Arias de Reyna integral

Producción CientíficaThe Moll-Arias de Reyna integral is generalized and several values are given.Ministerio de Economía, Industria y Competitividad (project MTM2014-57129-C2-1-P)Junta de Castilla y León (project VA057U16

A relativistic one dimensional band model with position dependent mass

Producción CientíficaIn this note a one-dimensional band model is proposed based on a periodic Dirac comb having a periodic mass distribution m(x). The mass function is represented as a Hermitian, non-local separable operator. Two specific cases–a constant mass model and a sinusoidal mass model–are examined. The lowest electron and positron bands for the constant mass case are similar to those for the standard relativistic Kronig-Penney model, suggesting that non-locality has little influence. The results for the sinusoidal case are consistent with the expectation that at low wavenumber an electron “feels” it has an average constant mass, but at high wave number, the particle “sees” the periodic mass variation and the band is distorted.Ministerio de Economía, Industria y Competitividad (project MTM2014-57129-C2-1-P)Junta de Castilla y León (project VA057U16

A note on the exact Green function for a quantum system decorated by two or more impurities

Producción CientíficaThe exact Green function is constructed for a quantum system, with known Green function, which is decorated by two delta function impurities. It is shown that when two such impurities coincide they behave as a single singular potential with combined amplitude. The results are extended to N impurities and higher dimensions.Ministerio de Economía, Industria y Competitividad (project ct MTM2014-57129-C2-1)Junta de Castilla y León (project VA057U

A functional identity involving elliptic integrals

Producción CientíficaWe show that adouble integral remains invariant as one trades some parameters. This invariance property is suggested from symmetry considerations in the operating characterstics of a semiconductor Hall-effect device.Ministerio de Economía, Industria y Competitividad (project MTM2014-57129-C2-1-P)Junta de Castilla y Leon (project UIC 0 11

Symmetries of certain double integrals related to Hall effect devices

Producción CientíficaOne encounters iterated elliptic integrals in the study of Hall effect devices, as a result of conformal mappings of Schwarz–Christoffel type. Some of these double elliptic integrals possess amazing symmetries with regard to the physical parameters of the underlying Hall effect devices. We give a unified mathematical treatment of such symmetric double integrals, in the context of Hall effect devices with three and four contacts.Junta de Castilla y León (VA057U16) and MINECO (Project MTM2014-57129-C2-1-P)