Malagutti, Marcello;
Parmeggiani, Alberto;
(2024)
Spectral quasi-clustering estimates for certain semiregular systems.
Bulletin des Sciences Mathematiques
, 193
, Article 103423. 10.1016/j.bulsci.2024.103423.
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Abstract
We show a quasi-clustering result for a subclass of the class of Semiregular Metric Globally Elliptic Systems (SMGES) including certain quantum optics models (such as Jaynes-Cummings and its generalizations) which describe light-matter interaction. More precisely, we show that for the class of systems with polynomial coefficients we consider, the spectrum concentrates within the union of intervals (not necessarily disjoint, but at most intersecting in an a priori finite number) centered at a sequence determined in terms of invariants of the (total) symbol and width decreasing as the centers go to infinity.
| Type: | Article |
|---|---|
| Title: | Spectral quasi-clustering estimates for certain semiregular systems |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.bulsci.2024.103423 |
| Publisher version: | https://doi.org/10.1016/j.bulsci.2024.103423 |
| Language: | English |
| Additional information: | © 2024 The Authors. Published by Elsevier Masson SAS under a Creative Commons license (http://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Spectral theory and eigenvalue problems for PDEs, Non-commutative harmonic oscillators, Weyl-calculus, Quasi-clustering |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10191201 |
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