Quantum unique ergodicity for magnetic Laplacians on T^2
Spectral Theory
2025-12-23 v2 Mathematical Physics
Analysis of PDEs
math.MP
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).
Keywords
Cite
@article{arxiv.2411.18449,
title = {Quantum unique ergodicity for magnetic Laplacians on T^2},
author = {Léo Morin and Gabriel Rivière},
journal= {arXiv preprint arXiv:2411.18449},
year = {2025}
}