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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.
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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


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  • HAL Id : hal-03136860, version 2


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⟩



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