Abstract
For two-dimensional Schrödinger operators with a nonzero constant magnetic field perturbed by an infinite number of periodically disposed, long-range magnetic and electric wells, it is proven that when the inter-well distance (R) grows to infinity, the essential spectrum near the eigenvalues of the ‘one well Hamiltonian’ is located in mini-bands whose widths shrink faster than any exponential with R. This should be compared with our previous result, which stated that, in the case of compactly supported wells, the mini-bands shrink Gaussian-like with R.
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Cornean, H.D. On the Essential Spectrum of Two-Dimensional Periodic Magnetic Schrödinger Operators. Letters in Mathematical Physics 49, 197–211 (1999). https://doi.org/10.1023/A:1007623907088
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DOI: https://doi.org/10.1023/A:1007623907088