https://doi.org/10.1140/epjb/e2019-100564-4
Regular Article
Localization in one-dimensional relativistic quantum mechanics
1
St. Xavier’s College,
Mumbai
400001, India
2
Nuclear Physics Division, Bhabha Atomic Research Centre,
Mumbai
400085, India
3
Homi Bhabha National Institute, Training School Complex, Anushakti Nagar,
Mumbai
400094, India
4
UM-DAE Centre for Excellence in Basic Sciences, University of Mumbai, Vidynagari Campus,
Mumbai
400098, India
a e-mail: sjoshi@barc.gov.in
Received:
20
November
2019
Published online: 3 February 2020
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.
Key words: Solid State and Materials
© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020