\(\mathscr {D}{-}\)Deformed and SUSY-Deformed Graphene: First Results

  • F. BagarelloEmail author
  • M. Gianfreda
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 184)


We discuss some mathematical aspects of two particular deformed versions of the Dirac Hamiltonian for graphene close to the Dirac points, one involving \(\mathscr {D}\)-pseudo bosons and the other supersymmetric quantum mechanics. In particular, in connection with \(\mathscr {D}\)-pseudo bosons, we show how biorthogonal sets arise, and we discuss when these sets are bases for the Hilbert space where the model is defined, and when they are not. For the SUSY extension of the model we show how this can be achieved and which results can be obtained.



F.B. acknowledges partial support by the University of Palermo and by G.N.F.N. The authors also wish to thank Prof. N. Hatano for many useful discussions.


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Dipartimento di Energia, Ingegneria dell’Informazione e Modelli Matematici Facoltà di IngegneriaUniversità di PalermoPalermoItaly
  2. 2.Institute of Industrial ScienceUniversity of TokyoMeguroJapan

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