Semiclassical Evolution With Low Regularity

François Golse (1) , Thierry Paul (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

We prove semiclassical estimates for the Schrödinger-von Neumann evolution with $C^{ 1,1}$ potentials and density matrices whose square root have either Wigner functions with low regularity independent of the dimension, or matrix elements between Hermite functions having long range decay. The estimates are settled in different weak topologies and apply to the N body quantum dynamics uniformly in N .

Domaines: Mathématiques [math]; Physique mathématique [math-ph]; Physique [physics]; Physique Quantique [quant-ph]

François Golse, Thierry Paul. Semiclassical Evolution With Low Regularity. 2020. ⟨hal-02619489v1⟩