97-642 Herbst I., Nakamura S.

Schr\"odinger operators with strong magnetic fields: Quasi-periodicity of spectral orbits and topology (65K, LATeX 2e) Dec 19, 97

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Abstract. We investigate the large $\lambda$ behavior of $\sigma((p-\lambda A)^2)$ when the zero set of $B = dA$ has a non-empty interior. With certain technical hypotheses we show that if either $B$ is bounded away from zero for large $|x|$ or periodic and certain quotients of standard homology groups are finite rank, then $\sigma((p-\lambda A)^2)$ approaches a quasi-periodic orbit in the space of subsets of $[0,\infty)$.

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