Skip to Main content Skip to Navigation
Journal articles

Time dependent Quantum Perturbations uniform in the semiclassical regime

Abstract : We present a time dependent quantum perturbation result, uniform in the Planck constant, for perturbations of potentials whose gradients are Lipschitz continuous by potentials whose gradients are only bounded a.e.. Though this low regularity of the full potential is not enough to provide the existence of the classical underlying dynamics, at variance with the quantum one, our result shows that the classical limit of the perturbed quantum dynamics remains in a tubular neighbourhood of the classical unperturbed one of size of order of the square root of the size of the perturbation. We treat both Schrödinger and von Neumann-Heisenberg equations.
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03136860
Contributor : Thierry Paul Connect in order to contact the contributor
Submitted on : Wednesday, March 17, 2021 - 9:17:43 PM
Last modification on : Saturday, December 4, 2021 - 4:09:10 AM

File

PotentialQuinquiesCor - essai5...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03136860, version 2

Citation

François Golse, Thierry Paul. Time dependent Quantum Perturbations uniform in the semiclassical regime. Indiana University Mathematics Journal, Indiana University Mathematics Journal, In press. ⟨hal-03136860v2⟩

Share

Metrics

Les métriques sont temporairement indisponibles