Semi-classical behaviour of Schrödinger's dynamics : revivals of wave packets on hyperbolic trajectory

Olivier Lablée (1)

1 IF - Institut Fourier

The aim of this paper is to study the semi-classical behaviour of Schrödinger's dynamics for an one-dimesional quantum Hamiltonian with a classical hyperbolic trajectory. As in the regular case (elliptic trajectory), we prove, that for an initial wave packets localized in energy, the dynamics follows the classical motion during short time. And, for large time, a new period for the dynamics appears : the wave packets revivals.

Mots clés: Schrödinger's dynamics; revivals of wave packets; semi-classical analysis; hypebolic trajectory; Schrödinger operator with double wells potential

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

Olivier Lablée. Semi-classical behaviour of Schrödinger's dynamics : revivals of wave packets on hyperbolic trajectory. 2010. ⟨hal-00443738v3⟩