2015/03/26 by Andrea Mantile, Mantile, Andrea · 1 citation
Mathematics · Physics and Astronomy · #35B25 #35C20 #35P25 #35Q40 #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum and electron transport phenomena #Spectral Theory in Mathematical Physics #Theoretical and Computational Physics #math-ph #math.AP #math.MP #msc:35B25 #msc:35C20 #msc:35P25 #msc:35Q40
paper · pdf · doi:10.48550/arxiv.1503.07701
21 pages, latex The paper has been withdrawn due to a crucial error in the proof of the Lemma 3.1
openalex publication_date 2015/03/26 · arxiv created 2015/08/31 · arxiv updated 2015/09/02 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28
We introduce a modified model where h-dependent artificial interface conditions, occurring at the boundary of an interaction region, allow to obtain adiabatic approximations for the relevant resonant states connected to the quantum transport problem. Under positivity assumptions on the potential, we show that this modification produces a small perturbation of the dynamics on any time scale. The result extends to the corresponding non-autonomous case, allowing us to consider the adiabatic evolution problem in the modified setting. In this framework, we give an expansion formula for the small-h asymptotics of the adiabatic variable, where the error introduced on the adiabatic dynamics by the interface conditions is polynomially small w.r.t. h, independently from the adiabatic time scale. This result provides with a rigorous mathematical framework for the interface conditions approach to the analysis of the adiabatic transport problem in the quantum wells regime.