03264nam 22006133 450 991096440690332120251117113944.097814704728011470472805(MiAaPQ)EBC30222569(Au-PeEL)EBL30222569(CKB)25289764400041(OCoLC)1350688349(EXLCZ)992528976440004120221110d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierAdiabatic Evolution and Shape Resonances1st ed.Providence :American Mathematical Society,2022.©2022.1 online resource (102 pages)Memoirs of the American Mathematical Society ;v.280Print version: Hitrik, Michael Adiabatic Evolution and Shape Resonances Providence : American Mathematical Society,c2022 9781470454210 "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"--Provided by publisher.Memoirs of the American Mathematical Society Mathematical physicsAdiabatic invariantsPartial differential equations -- Qualitative properties of solutions -- ResonancesmscPartial differential equations -- Elliptic equations and systems -- Schrödinger operatormscPartial differential equations -- Spectral theory and eigenvalue problems -- Asymptotic distribution of eigenvalues and eigenfunctionsmscPartial differential equations -- Pseudodifferential operators and other generalizations of partial differential operators -- Pseudodifferential operatorsmscMathematical physics.Adiabatic invariants.Partial differential equations -- Qualitative properties of solutions -- Resonances.Partial differential equations -- Elliptic equations and systems -- Schrödinger operator.Partial differential equations -- Spectral theory and eigenvalue problems -- Asymptotic distribution of eigenvalues and eigenfunctions.Partial differential equations -- Pseudodifferential operators and other generalizations of partial differential operators -- Pseudodifferential operators.515/.7242515.724235B3435J1035P2035S05mscHitrik Michael1802077Mantile Andrea1802078Sjöstrand J(Johannes)351203MiAaPQMiAaPQMiAaPQBOOK9910964406903321Adiabatic Evolution and Shape Resonances4347611UNINA