Quantum limits of the Martinet sub-Laplacian

Víctor Arnaiz

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arXiv · 2505.19326

Quantum limits of the Martinet sub-Laplacian

Víctor Arnaiz

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Abstract

In this article we study the semiclassical asymptotics of the Martinet sub-Laplacian on the flat toroidal cylinder $M = \mathbb{R} \times \mathbb{T}^2$. We describe the asymptotic distribution of sequences of eigenfunctions oscillating at different scales prefixed by Rothschild-Stein estimates via the introduction of adapted two-microlocal semiclassical measures. We obtain concentration and invariance properties of these measures in terms of effective dynamics governed by harmonic or an-harmonic oscillators depending on the regime, and we show additional regularity properties with respect to critical points of the eigenvalues of the Montgomery family of quartic oscillators.

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Víctor Arnaiz. 2025-05-25. Quantum limits of the Martinet sub-Laplacian. https://arxiv.org/abs/2505.19326

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