The EMS Publishing House is now EMS Press and has its new home at ems.press.
Please find all EMS Press journals and articles on the new platform.
Journal of Spectral Theory
Full-Text PDF (372 KB) | Metadata |
Table of Contents | JST summary
Published online: 2018-10-23
Spectral flow for skew-adjoint Fredholm operators
Alan L. Carey[1], John Phillips[2] and Hermann Schulz-Baldes[3] (1) Australian National University, Canberra, Australia and University of Wollongong, Australia(2) University of Victoria, Canada
(3) Universität Erlangen-Nürnberg, Germany
An analytic definition of a $\mathbb Z_2$-valued spectral flow for paths of real skew-adjoint Fredholm operators is given. It counts the parity of the number of changes in the orientation of the eigenfunctions at eigenvalue crossings through 0 along the path. The $\mathbb Z_2$-valued spectral flow is shown to satisfy a concatenation property and homotopy invariance, and it provides an isomorphism on the fundamental group of the real skew-adjoint Fredholm operators. Moreover, it is connected to a $\mathbb Z_2$-index pairing for suitable paths. Applications concern the zero energy bound states at defects in a Majorana chain and a spectral flow interpretation for the $\mathbb Z_2$-polarization in these models.
Keywords: Spectral flow, skew-symmetric operators, topological insulators
Carey Alan, Phillips John, Schulz-Baldes Hermann: Spectral flow for skew-adjoint Fredholm operators. J. Spectr. Theory 9 (2019), 137-170. doi: 10.4171/JST/243