Abstract:This paper is dedicated to the proof of a Quantum Ergodicity (QE) theorem for the eigenfunctions of subLaplacians on contact metric manifolds, under the assumption that the Reeb flow is ergodic. To do so, we rely on a semiclassical pseudodifferential calculus developed for general filtered manifolds that we specialize to the setting of contact manifolds. Our strategy is then reminiscent of an implementation of the Born-Oppenheimer approximation as we rely on the construction of microlocal projectors in our calculus which commute with the subLaplacian, called Landau projectors. The subLaplacian is then shown to act effectively on the range of each Landau projector as the Reeb vector field does. The remainder of the proof follows the classical path towards QE, once microlocal Weyl laws have been established.
| Subjects: | Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Spectral Theory (math.SP) |
| Cite as: | arXiv:2507.18216 [math.AP] |
| (or arXiv:2507.18216v4 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2507.18216 arXiv-issued DOI via DataCite |
From: Lino Benedetto [view email]
[v1]
Thu, 24 Jul 2025 09:11:35 UTC (50 KB)
[v2]
Fri, 25 Jul 2025 16:53:16 UTC (50 KB)
[v3]
Thu, 18 Sep 2025 08:53:51 UTC (50 KB)
[v4]
Fri, 22 May 2026 14:01:22 UTC (52 KB)
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