KAM Hamiltonians are not Quantum Ergodic

Abstract

We show that under generic conditions, the quantisation of a $1$-parameter family of KAM perturbations $P(x,\xi ;t)$ 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 $t\in (0,\delta )$.

arXiv admin note: substantial text overlap with arXiv:1709.09919

References in corpus (2)

• Weyl's law and quantum ergodicity for maps with divided phase space
• KAM Theorem for Gevrey Hamiltonians