Journal of Spectral Theory
Full-Text PDF (637 KB) | Metadata |
Table of Contents | JST summary
Published online: 2014-03-16
Quantum ergodicity for a class of mixed systems
Jeffrey Galkowski[1] (1) University of California Berkeley, USAWe examine high energy eigenfunctions for the Dirichlet Laplacian on domains where the billiard flow exhibits mixed dynamical behavior. (More generally, we consider semiclassical Schrödinger operators with mixed assumptions on the Hamiltonian flow.) Specifically, we assume that the billiard flow has an invariant ergodic component, $U$, and study defect measures, $\mu$, of positive density subsequences of eigenfunctions (and, more generally, of almost orthogonal quasimodes). We show that any defect measure associated to such a subsequence satisfies $\mu|_{U}=c\mu_L|_{U}$, where $\mu_L$ is the Liouville measure. This proves part of a conjecture of Percival [18].
Keywords: quantum ergodicity, mixed dynamics, semiclassical
Galkowski Jeffrey: Quantum ergodicity for a class of mixed systems. J. Spectr. Theory 4 (2014), 65-85. doi: 10.4171/JST/62