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Behavior of the spectrum of the periodic Schrodinger operators near the edges of the gaps

Date: 
Wednesday 24th June 2015 - 13:30 to 14:30
Venue: 
INI Seminar Room 1
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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons