Institute for Mathematical Physics on the Essential Spectrum of Two Dimensional Periodic Magnetic Schrr Odinger Operators on the Essential Spectrum of Two Dimensional Periodic Magnetic Schrr Odinger Operators
نویسنده
چکیده
For two dimensional Schrr odinger operators with a nonzero constant magnetic eld perturbed by an innnite number of periodically disposed, long range magnetic and electric wells, it is proven that when the inter-well distance (R) grows to innnity, the essential spectrum near the eigenvalues of the \one well Hamiltonian" is located in mini-bands whose width shrink faster than any exponential with R. This should be compared with our previous result 5], which stated that in the case of compactly supported wells, the mini-bands shrink Gaussian like with R.
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