@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

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              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.
            """ ;
    dct:identifier "hal-00617372" ;
    dct:issued "2026-05-24T06:47:51.234937"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-24T06:47:51.234942"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Semiclassical approximation and noncommutative geometry" ;
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    dcat:keyword "infoeu-reposemanticspreprint",
        "mathmath-apmathematics-mathanalysis-of-pdes-mathap",
        "preprints-working-papers-" ;
    dcat:landingPage <https://hal.science/hal-00617372> .

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    dct:issued "2026-05-24T06:47:51.242492"^^xsd:dateTime ;
    dct:modified "2026-05-24T06:47:51.224493"^^xsd:dateTime ;
    dct:title "Semiclassical approximation and noncommutative geometry" ;
    dcat:accessURL <https://hal.science/hal-00617372> .

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