Quantum unique ergodicity for magnetic Laplacians on T^2

Léo Morin; Gabriel Rivière

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arXiv · 2411.18449

Quantum unique ergodicity for magnetic Laplacians on T^2

Léo Morin·Gabriel Rivière

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Abstract

Given a smooth integral two-form and a smooth potential on the flat torus of dimension 2, we study the high energy properties of the corresponding magnetic Schr\"odinger operator. Under a geometric condition on the magnetic field, we show that every sequence of high energy eigenfunctions satisfies the quantum unique ergodicity property even if the Liouville measure is not ergodic for the underlying classical flow (the Euclidean geodesic flow on the 2-torus).

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Léo Morin, Gabriel Rivière. 2024-11-27. Quantum unique ergodicity for magnetic Laplacians on T^2. https://arxiv.org/abs/2411.18449

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