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Invariance of IDS under Darboux transformation and its application

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Periodic and Ergodic Spectral Problems

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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