Adiabatic evolution and shape resonances

Adiabatic evolution and shape resonances

Motivated by a problem of one mode approximation for a non-linear evolution with charge accumulation in potential wells, we consider a general linear adiabatic evolution problem for a semi-classical Schrodinger operator with a time dependent potential with a well in an island. In particular, we show...

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Détails bibliographiques
Auteurs principaux : Hitrik Michael (Auteur), Mantile Andrea (Auteur), Sjöstrand Johannes (Auteur)
Format : Livre
Langue : anglais
Titre complet : Adiabatic evolution and shape resonances / Michael Hitrik, Andrea Mantile, Johannes Sjöstrand
Publié : Providence (R.I.) : American Mathematical Society , 2022
Description matérielle : 1 vol. (V-90 p.)
Collection : Memoirs of the American Mathematical Society ; 1380
Sujets :
Physique mathématique
Invariants adiabatiques
Équations aux dérivées partielles
Description
Résumé : Motivated by a problem of one mode approximation for a non-linear evolution with charge accumulation in potential wells, we consider a general linear adiabatic evolution problem for a semi-classical Schrodinger operator with a time dependent potential with a well in an island. In particular, we show that we can choose the adiabatic parameter with ln , where h denotes the semi-classical parameter, and get adiabatic approximations of exact solutions over a time interval of length N with an error O(). Here N 0 is arbitrary.
Notes : "November 2022, volume 280, number 1380 (third of 8 numbers)"
Bibliographie : Bibliogr. p. 89-90
ISBN : 978-1-4704-5421-0