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Bispectral Duality of Integrable Particle Systems Kasman, Alex
Description
Two particle systems are said to be “dual” if the maps that linearize their dynamics are inverses. “Bispectrality", on the other hand, describes the situation in which a function satisfies two eigenvalue equations with the roles of spacial and spectral variables exchanged. Although bispectrality does not initially appear to be dynamical in nature, it turns out that duality manifests itself as bispectrality on both the classical and quantum levels. (For example, the Calogero-Moser system is self-dual since its action-angle map is an involution, and this can be seen either in a symmetry of the eigenfunction of its quantum Hamiltonian or through the appearance of this particle system in the pole dynamics of bispectral solutions of the KP Hierarchy.) This talk will review both old and recent results on this subject and then conclude with a list of associated open problems.
Item Metadata
Title |
Bispectral Duality of Integrable Particle Systems
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-06-17T09:01
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Description |
Two particle systems are said to be “dual” if the maps that linearize their dynamics are inverses. “Bispectrality", on the other hand, describes the situation in which a function satisfies two eigenvalue equations with the roles of spacial and spectral variables exchanged. Although bispectrality does not initially appear to be dynamical in nature, it turns out that duality manifests itself as bispectrality on both the classical and quantum levels. (For example, the Calogero-Moser system is self-dual since its action-angle map is an involution, and this can be seen either in a symmetry of the eigenfunction of its quantum Hamiltonian or through the appearance of this particle system in the pole dynamics of bispectral solutions of the KP Hierarchy.) This talk will review both old and recent results on this subject and then conclude with a list of associated open problems.
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Extent |
42 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: College of Charleston
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Series | |
Date Available |
2017-01-29
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0340393
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International