2017/11/21 by Michael Hitrik, Hitrik, Michael, Andrea Mantile +3
Mathematics · #35B34 #35J10 #35P20 #35S05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1711.07583
openalex publication_date 2017/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Schrödinger operator with a time dependent potential with a well in an island. In particular, we show that we can choose the adiabatic parameter ε with lnε \asymp -1/h, where h denotes the semi-classical parameter, and get adiabatic approximations of exact solutions over a time interval of length ε -N with an error \cal O(ε N). Here N>0 is arbitrary.