Investigación

 

Dirac comb with a periodic mass jump

 

J.J. Alvarez^a, M. Gadella^b, L.M. Nieto^c

 

^a E.U. de Informática de Segovia, University of Valladolid, Spain. jjalvarez@infor.uva.es

^b Departamento de Física Teórica, Atómica y Optica, Universidad de Valladolid, Facultad de Ciencias, Paseo Belén 9, 47011, Valladolid, Spain. e-mail: manuelgadella1@gmail.com

^c Física Teórica, Atómica y Optica, Universidad de Valladolid, Facultad de Ciencias, Paseo Belén 9, 47011, Valladolid, Spain. e-mail: luismi@metodos.fam.cie.uva.es

 

Received 3 June 2013
Accepted 26 July 2013

 

Abstract

We discuss some of the properties of the spectrum of a Dirac comb with periodic mass discontinuity. Based on the relationship between the two different masses, we derive the general behavior of the spectra for both cases E > 0 and E < 0. The relationship with the constant mass model for the Dirac comb and the generalization to periodic quantum chains with n different masses are also discussed.

Keywords: Delta interactions; mass jumps; periodic potentials; energy band structures.

 

Resumen

Se discuten algunas de las propiedades del espectro del peine de Dirac con una discontinuidad periódica en la masa. Deducimos el comportamiento general del espectro para los casos E > 0 and E < 0, basándonos en la relación entre las diferentes masas. También se discute la correspondencia entre nuestros resultados y los obtenidos para el peine de Dirac con masa constante, así como la generalización a cadenas periódicas con n masas diferentes.

Descriptores: Interacciones tipo delta; saltos de masa; potenciales periódicos; estructuras de bandas de energía.

 

PACS: 03.65.-w; 03.65.Ge

 

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Acknowledgements

We wish to acknowledge partial financial support by the Spanish Ministry of Science and Innovation through Project MTM2009-10751, the Junta de Castilla y León, through Project GR224.

 

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