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Localization in one-dimensional relativistic quantum mechanics

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Abstract

We present the relativistic analogue of Anderson localization in one dimension. We use Dirac equation to calculate the transmission probability for a spin-½ particle incident upon a rectangular barrier. Using the transfer matrix formalism, we numerically compute the transmission probability for the case of a large number of identical barriers spread randomly in one dimension. The particular case when the incident particle has three component momentum and shows spin-flip phenomena is also considered. Our calculations suggest that the incident relativistic particle shows localization behaviour similar to that of Anderson localization. A number of results which are generalizations of the non-relativistic case are also obtained.

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Authors and Affiliations

  1. St. Xavier’s College, Mumbai, 400001, India

    Abhay Mehta

  2. Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai, 400085, India

    Sandeep Joshi & Sudhir R. Jain

  3. Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai, 400094, India

    Sandeep Joshi & Sudhir R. Jain

  4. UM-DAE Centre for Excellence in Basic Sciences, University of Mumbai, Vidynagari Campus, Mumbai, 400098, India

    Sudhir R. Jain

Authors
  1. Abhay Mehta
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  2. Sandeep Joshi
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  3. Sudhir R. Jain
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Correspondence to Sandeep Joshi.

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Mehta, A., Joshi, S. & Jain, S.R. Localization in one-dimensional relativistic quantum mechanics. Eur. Phys. J. B 93, 20 (2020). https://doi.org/10.1140/epjb/e2019-100564-4

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  • DOI: https://doi.org/10.1140/epjb/e2019-100564-4

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