Upper bounds on the rate of quantum ergodicity

@inproceedings{Schubert2005UpperBO,
  title={Upper bounds on the rate of quantum ergodicity},
  author={Roman Schubert},
  year={2005}
}
We study the semiclassical behaviour of eigenfunctions of quantum systems with ergodic classical limit. By the quantum ergodicity theorem almost all of these eigenfunctions become equidistributed in a weak sense. We give a simple derivation of an upper bound of order |ln ~|−1 on the rate of quantum ergodicity if the classical system is ergodic with a certain rate. In addition we obtain a similar bound on transition amplitudes if the classical system is weak mixing. Both results generalise… CONTINUE READING