Behavior of the spectrum of the periodic Schrodinger operators near the edges of the gaps
Duration: 56 mins 26 secs
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About this item
| Description: |
Shterenberg, R (University of Alabama at Birmingham)
Wednesday 24 June 2015, 13:30-14:30 |
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| Created: | 2015-06-30 16:38 |
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| Collection: | Periodic and Ergodic Spectral Problems |
| Publisher: | Isaac Newton Institute |
| Copyright: | Shterenberg, R |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Co-author: Leonid Parnovski (UCL)
It is a common belief that generically all edges of the spectrum of periodic Schrodinger operators are non-degenerate, i.e. are attained by a single band function at finitely many points of quasi-momentum and represent a non-degenerate quadratic minimum or maximum. We present the construction which shows that all degenerate edges of the spectrum can be made non-degenerate under arbitrary small perturbation. The corresponding perturbation is found in the class of potentials with larger (but proportional) periods; thus the final operator is still periodic but the lattice of periods changes. |
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