Semiclassical approximation and noncommutative geometry
type: Dataset
description: We consider the long time semiclassical evolution for the linear Schrödinger equation. We show that, in the case of chaotic underlying classical dynamics and for times up to $\hbar^{-2+\epsilon},\ \epsilon>0$, the symbol of a propagated observable by the corresponding von Neumann-Heisenberg equation is, in a sense made precise below, precisely obtained by the push-forward of the symbol of the observable at time $t=0$. The corresponding definition of the symbol calls upon a kind of Toeplitz quantization framework, and the symbol itself is an element of the noncommutative algebra of the (strong) unstable foliation of the underlying dynamics.
issued: 2026-05-24T06:47:51.234937
language: en
modified: 2026-05-24T06:47:51.234942
contact point: Organization
  fn: CCSD
keyword: infoeu-reposemanticspreprint
keyword: mathmath-apmathematics-mathanalysis-of-pdes-mathap
keyword: preprints-working-papers-
landing page: https://hal.science/hal-00617372

Semiclassical approximation and noncommutative geometry
type: Distribution
format: HTML
issued: 2026-05-24T06:47:51.242492
modified: 2026-05-24T06:47:51.224493
access URL: https://hal.science/hal-00617372

test_moissonnage_selune
type: Agent