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Article Dans Une Revue Indiana University Mathematics Journal Année : 2021

Time dependent Quantum Perturbations uniform in the semiclassical regime

Résumé

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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Dates et versions

hal-03136860 , version 1 (09-02-2021)
hal-03136860 , version 2 (17-03-2021)

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  • HAL Id : hal-03136860 , version 2

Citer

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