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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