Dirac operator spectrum in tubes and layers with a zigzag type boundary

Abstract

We derive a number of spectral results for Dirac operators in geometrically nontrivial regions in R 2 and R 3 of tube or layer shapes with a zigzag type boundary using the corresponding properties of the Dirichlet Laplacian.

Dirichlet Fractional Laplacian in multi-tubes

“…For the relativistic case, we know only two recent works [14] and [15] which discuss the similar problem for the Dirac operator −i∇. However, we stress that in contrast to A Ω s , this operator is local.…”