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Topological boundary invariants for Floquet systems and quantum walks. (English) Zbl 1413.46061
Summary: A Floquet systems is a periodically driven quantum system. It can be described by a Floquet operator. If this unitary operator has a gap in the spectrum, then one can define associated topological bulk invariants which can either depend only on the bands of the Floquet operator or also on the time as a variable. It is shown how a \(K\)-theoretic result combined with the bulk-boundary correspondence leads to edge invariants for the half-space Floquet operators. These results also apply to topological quantum walks.

MSC:
46L80 \(K\)-theory and operator algebras (including cyclic theory)
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
37L05 General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations
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