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Journal Articles J.Phys.A Year : 2022

Time and band limiting operator and Bethe ansatz

P.-A. Bernard
  • Function : Author
N. Crampe
  • Function : Author
L. Vinet
  • Function : Author

Abstract

The time and band limiting operator is introduced to optimize the reconstruction of a signal from only a partial part of its spectrum. In the discrete case, this operator commutes with the so-called algebraic Heun operator which appears in the context of the quantum integrable systems. The construction of both operators and the proof of their commutativity is recalled. A direct connection between their spectra is obtained. Then, the Bethe ansatz, a well-known method to diagonalize integrable quantum Hamiltonians, is used to diagonalize the Heun operator and to obtain insights on the spectrum of the time and band limiting operator.
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Dates and versions

hal-03546837 , version 1 (11-10-2022)

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P.-A. Bernard, N. Crampe, L. Vinet. Time and band limiting operator and Bethe ansatz. J.Phys.A, 2022, 55 (28), pp.285201. ⟨10.1088/1751-8121/ac7486⟩. ⟨hal-03546837⟩

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