Spectral flow for real skew-adjoint Fredholm operators

Autor:	Carey, Alan L., Phillips, John, Schulz-Baldes, Hermann
Rok vydání:	2016
Předmět:	Mathematical Physics Mathematics - Functional Analysis
Druh dokumentu:	Working Paper
Popis:	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. Comment: final corrections before publication in J. Spectral Theory
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1604.06994 Zobrazit plný text záznamu View this record from Arxiv