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Microlocal analysis of the bulk-edge correspondence. (English) Zbl 1462.81214

Summary: The bulk-edge correspondence predicts that interfaces between topological insulators support robust currents. We prove this principle for PDEs that are periodic away from an interface. Our approach relies on semiclassical methods. It suggests novel perspectives for the analysis of topologically protected transport.

MSC:

81V70 Many-body theory; quantum Hall effect
35J10 Schrödinger operator, Schrödinger equation
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
35Q40 PDEs in connection with quantum mechanics
82D20 Statistical mechanics of solids
35P05 General topics in linear spectral theory for PDEs
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
35P20 Asymptotic distributions of eigenvalues in context of PDEs
35S05 Pseudodifferential operators as generalizations of partial differential operators
46L87 Noncommutative differential geometry
19L10 Riemann-Roch theorems, Chern characters
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