Stability of gaps for periodic potentials under variation of a magnetic field. (English) Zbl 0586.35084

Let \(H_ 0(B)\) denote the Hamiltonian of a free electron in a magnetic field B. Let V be a periodic potential. We show that if an interval [a,b] is not in the spectrum of \(H_ 0(B_ 0)+V\) for some \(B_ 0\), then it is not in the spectrum for all B sufficiently close to \(B_ 0\).


35Q99 Partial differential equations of mathematical physics and other areas of application
35B10 Periodic solutions to PDEs
35P15 Estimates of eigenvalues in context of PDEs
35B37 PDE in connection with control problems (MSC2000)
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