Random Dirac operators with time-reversal symmetry

Details Random Dirac operators with time-reversal symmetry Random Dirac operators with time-reversal symmetry

2009-02-11

arxiv.org/abs/0902.1935v2

Commun. Math. Phys. 295, 209-242 (2010)

Physics

Mathematical Physics

parts of introduction made more precise, corrections as follow-up on referee reports

Scientific paper

10.1007/s00220-009-0956-4

Quasi-one-dimensional stochastic Dirac operators with an odd number of channels, time reversal symmetry but otherwise efficiently coupled randomness are shown to have one conducting channel and absolutely continuous spectrum of multiplicity two. This follows by adapting the criteria of Guivarch-Raugi and Goldsheid-Margulis to the analysis of random products of matrices in the group SO$^*(2L)$, and then a version of Kotani theory for these operators. Absence of singular spectrum can be shown by adapting an argument of Jaksic-Last if the potential contains random Dirac peaks with absolutely continuous distribution.

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