Graph Eigenfunctions and Quantum Unique Ergodicity

Details Graph Eigenfunctions and Quantum Unique Ergodicity Graph Eigenfunctions and Quantum Unique Ergodicity

2010-06-18

arxiv.org/abs/1006.3583v1

Mathematics

Dynamical Systems

8 pages

Scientific paper

We apply the techniques of our previous paper to study joint eigenfunctions of the Laplacian and one Hecke operator on compact congruence surfaces, and joint eigenfunctions of the two partial Laplacians on compact quotients of $\mathbb{H}\times\mathbb{H}$. In both cases, we show that quantum limit measures of such sequences of eigenfunctions carry positive entropy on almost every ergodic component. Together with prior work of the second named author, this implies Quantum Unique Ergodicity for such functions.

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