Quantum ergodicity for restrictions to hypersurfaces
  Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is a hypersurface in the position space satisfying a simple dynamical condition, the restrictions of eigenstates to N are also quantum ergodic. 
Semyon Dyatlov and Maciej Zworski
math.AP math.SP