A quantum pseudo-integrable Hamiltonian impact system
Abstract
Quantization of a toy model of a pseudointegrable Hamiltonian impact system is introduced, including EBK quantization conditions, a verification of Weyl's law, the study of their wavefunctions and a study of their energy levels properties. It is demonstrated that the energy levels statistics are similar to those of pseudointegrable billiards. Yet, here, the density of wavefunctions which concentrate on projections of classical level sets to the configuration space does not disappear at large energies, suggesting that there is no equidistribution in the configuration space in the large energy limit; this is shown analytically for some limit symmetric cases and is demonstrated numerically for some nonsymmetric cases.
Cite
@article{arxiv.2304.09455,
title = {A quantum pseudo-integrable Hamiltonian impact system},
author = {Omer Yaniv},
journal= {arXiv preprint arXiv:2304.09455},
year = {2023}
}
Comments
Master Thesis advised by Vered Rom-Kedar. arXiv admin note: substantial text overlap with arXiv:2210.02854