Thursday, April 12, 2012

1204.2276 (M. I. Katsnelson et al.)

The Aharonov-Bohm effect for massless Dirac fermions and the spectral
flow of Dirac type operators with classical boundary conditions
   [PDF]

M. I. Katsnelson, V. E. Nazaikinskii
We compute, in topological terms, the spectral flow of an arbitrary family of self-adjoint Dirac type operators with classical (local) boundary conditions on a compact Riemannian manifold with boundary under the assumption that the initial and terminal operators of the family are conjugate by a bundle automorphism. This result is used to study conditions for the existence of nonzero spectral flow of a family of self-adjoint Dirac type operators with local boundary conditions in a two-dimensional domain with nontrivial topology. Possible physical realizations of nonzero spectral flow are discussed.
View original: http://arxiv.org/abs/1204.2276

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