Semiclassical behaviour of quantum eigenstates
Mathematical Physics
2019-05-30 v1 Analysis of PDEs
math.MP
Spectral Theory
Quantum Physics
Abstract
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures. We mostly focus on two opposite dynamical paradigms: completely integrable systems and chaotic ones. We recall standard tools from microlocal analysis and from dynamical systems. We show how to use them in order to illustrate the classical-quantum correspondance and to compare properties of completely integrable and chaotic systems.
Cite
@article{arxiv.1905.12303,
title = {Semiclassical behaviour of quantum eigenstates},
author = {Gabriel Rivière},
journal= {arXiv preprint arXiv:1905.12303},
year = {2019}
}
Comments
Lecture notes for the Spring School ''From quantum to classical'' (CIRM, April 2019)