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arXiv · 1905.12303

Semiclassical behaviour of quantum eigenstates

Gabriel Rivière
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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.

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Gabriel Rivière. 2019-05-29. Semiclassical behaviour of quantum eigenstates. https://arxiv.org/abs/1905.12303

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