English

KAM Hamiltonians are not Quantum Ergodic

Analysis of PDEs 2023-04-26 v2

Abstract

We show that under generic conditions, the quantisation of a 11-parameter family of KAM perturbations P(x,ξ;t)P(x,\xi;t) of a completely integrable and Kolmogorov non-degenerate Gevrey smooth Hamiltonian is not quantum ergodic, at least for a full measure subset of the parameter t(0,δ)t\in (0,\delta).

Cite

@article{arxiv.1811.07718,
  title  = {KAM Hamiltonians are not Quantum Ergodic},
  author = {Sean Gomes},
  journal= {arXiv preprint arXiv:1811.07718},
  year   = {2023}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1709.09919

R2 v1 2026-06-23T05:20:33.686Z