Title

Spectral flow for skew-adjoint Fredholm operators

RIS ID

132851

Publication Details

Carey, A. L., Phillips, J. & Schulz-Baldes, H. (2019). Spectral flow for skew-adjoint Fredholm operators. Journal of Spectral Theory, 9 (1), 137-170.

Abstract

An analytic definition of a Z2-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 Z2-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 Z2-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 Z2-polarization in these models.

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Link to publisher version (DOI)

http://dx.doi.org/10.4171/JST/243