Solitons of general topological charge over noncommutative tori
Peer reviewed, Journal article
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Original versionReviews in Mathematical Physics. 2021, 33 . 10.1142/S0129055X21500094
We study solitons of general topological charge over noncommutative tori from the perspective of time-frequency analysis. These solitons are associated with vector bundles of higher rank, expressed in terms of vector-valued Gabor frames. We apply the duality theory of Gabor analysis to show that Gaussians are such solitons for any value of a topological charge. Also they solve self/anti-self duality equations resulting from an energy functional for projections over noncommutative tori, and have a reformulation in terms of Gabor frames. As a consequence, the projections generated by Gaussians minimize the energy functional. We also comment on the case of the Moyal plane and the associated continuous vector-valued Gabor frames and show that Gaussians are the only class of solitons there.