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Almost periodic chains (models for incommensurate phases) and quasiperiodic chains (models for quasicrystals) have a richer topological phase structure than periodic chains, due to the existence of phasons. This effects the bulk boundary correspondence for these models. We investigate in particular quasiperiodic chains where the phason degree of freedom lives in a totally disconnected space. We show how we can nevertheless define a winding number for the boundary resonances and thus obtain an equation which relates the integrated density of states at a gap to a winding number which can be interpreted as the work the phason motion exhibits on the edge states of the system.

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Johannes Kellendonk, Institut Camille Jordan (Lyon)
Stefan Cohn‐Vossen Raum des Mathematischen Instituts (Raum 313)
Contact: Christopher Max