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Invariance of IDS under Darboux transformation and its application

Date: 
Wednesday 24th June 2015 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
The integrated density of states (IDS) is a crucial quantity for studying spectral properties of ergodic Schroedinger opearators. Especially in one dimension it determines most of the spectral properties. On the other hand, in relation to completely integrable systems, Darboux transformation has been investigated from various points of views. In this talk the invariance of IDS under Darboux transformation will be shown, and as a byproduct the invariance of IDS under KdV flow will be remarked.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons