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Slepian eigenvalues as tunnelling rates

Creagh, Stephen C.; Gradoni, Gabriele

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Gabriele Gradoni


We calculate the eigenvalues of an integral operator associated with Prolate Spheroidal Wave Functions (or Slepian functions) by interpreting them as tunnelling probabilities in an analogous quantum problem. Doing so allows us to extend a well-known approximation due to Slepian so that it applies outside an important transition region where these eigenvalues pass from being near unity to being near zero. Study of the eigenvalues has traditionally been associated with problems arising in signal analysis and optics but have more recently found relevance in quantifying the channel strengths available to Multiple-In Multiple-Out (MIMO) radio communication. The approach presented promises easier generalisation to the broader range of geometries possible in the latter context.


Creagh, S. C., & Gradoni, G. (2023). Slepian eigenvalues as tunnelling rates. Annals of Physics, 449, Article 169204.

Journal Article Type Article
Acceptance Date Dec 21, 2022
Online Publication Date Dec 26, 2022
Publication Date Feb 1, 2023
Deposit Date Feb 6, 2023
Publicly Available Date Feb 6, 2023
Journal Annals of Physics
Print ISSN 0003-4916
Electronic ISSN 1096-035X
Publisher Elsevier BV
Peer Reviewed Peer Reviewed
Volume 449
Article Number 169204
Keywords Tunnelling; WKB; Slepian; Holographic; MIMO; Communication
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