Generalized quantum unique ergodicity conjecture for ergodic flows and maps

Let $\Phi^t_H$ be an ergodic Hamiltonian flow on an energy shell $\mathcal{E}_E$, with quantum Hamiltonian $\hat H_\hbar$ and eigenstates $\psi_{\hbar,j}$ of energies $E_{\hbar,j}\approx E$. Let $\kappa$ be a canonical ergodic map on the torus $\mathbb{T}^2$, and let $(U_N(\kappa))_{N\in\mathbb{N}}$ be an associated quantum map. Generalized quantum unique ergodicity conjecture. All eigenstates $\psi_{\hbar,j}$ with $E_{\hbar,j}\approx E$ become equidistributed as $\hbar\to0$, and all eigenstates of $U_N(\kappa)$ become equidistributed on $\mathbb{T}^2$ as $N\to\infty$. This extends QUE from negatively curved geodesic flows to ergodic Hamiltonian flows and canonical maps; the supplied source gives no resolution.