Random Dirac operators with time-reversal symmetry

Abstract

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${}^{\ast }(2L)$, 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.

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

References in corpus (3)

• Anderson Transitions
• Rotation numbers for Jacobi matrices with matrix entries
• Localization for a matrix-valued Anderson model

Cited by in corpus (14)

• Topological invariants of edge states for periodic two-dimensional models
• Persistence of spin edge currents in disordered quantum spin Hall systems
• Absolutely Continuous Spectrum for Random Schroedinger Operators on the Bethe Strip
• Lyapunov spectra for all symmetry classes of quasi-one-dimensional disordered systems of non-interacting Fermions
• Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel
• The random phase property and the Lyapunov spectrum for disordered multi-channel systems
• Absolutely Continuous Spectrum for random Schroedinger operators on the Fibonacci and similar tree-strips
• Absolutely Continuous Spectrum for Random Schroedinger Operators on Tree-Strips of finite cone type
• Multiplicity bound of Singular Spectrum for higher rank Anderson models
• A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes
• Multiplicity theorem of singular Spectrum for general Anderson type Hamiltonian
• Localization for one-dimensional Anderson-Dirac models
• Jakšić-Last Theorem for Higher Rank Perturbations
• On multiplicity of spectrum for Anderson type operators with higher rank perturbations