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

Avron, J.; Simon, B.

J. Phys. A 18, 2199-2205 (1985).

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 \(B_ 0\).

MSC:

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)

Keywords:

Hamiltonian; free electron in a magnetic field; periodic potential; spectrum