Semiclassical behaviour of quantum eigenstates

Gabriel Rivière (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Domaines: Physique mathématique [math-ph]; Théorie spectrale [math.SP]; Equations aux dérivées partielles [math.AP]

Gabriel Rivière. Semiclassical behaviour of quantum eigenstates. 2019. ⟨hal-02141621⟩