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Localization in one-dimensional relativistic quantum mechanics

Author

Listed:
  • Abhay Mehta

    (St. Xavier’s College)

  • Sandeep Joshi

    (Nuclear Physics Division, Bhabha Atomic Research Centre
    Homi Bhabha National Institute, Training School Complex, Anushakti Nagar)

  • Sudhir R. Jain

    (Nuclear Physics Division, Bhabha Atomic Research Centre
    Homi Bhabha National Institute, Training School Complex, Anushakti Nagar
    UM-DAE Centre for Excellence in Basic Sciences, University of Mumbai, Vidynagari Campus)

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. Graphical abstract

Suggested Citation

  • Abhay Mehta & Sandeep Joshi & Sudhir R. Jain, 2020. "Localization in one-dimensional relativistic quantum mechanics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(2), pages 1-9, February.
    • Handle: RePEc:spr:eurphb:v:93:y:2020:i:2:d:10.1140_epjb_e2019-100564-4
    DOI: 10.1140/epjb/e2019-100564-4
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    Solid State and Materials;

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