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Semiclassical Evolution With Low Regularity

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 نشر من قبل Thierry Paul
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English
 تأليف Franc{c}ois Golse




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We prove semiclassical estimates for the Schrodinger-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 initial density operators whose square root have Wigner functions $7$ times differentiable, independently of the dimension. They also apply to the $N$ body quantum dynamics uniformly in $N$. In a appendix, we finally estimate the dependence in the dimension of the constant appearing on the Calderon-Vaillancourt Theorem.



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