2005/10/25 by Grégoire Allaire, Gregoire Allaire, Allaire, Gregoire +2
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 35B27 #Secondary: 35Q40 #math-ph #math.MP #msc:35B27 #msc:35Q40
paper · pdf · doi:10.48550/arxiv.math-ph/0510083
arxiv created 2005/10/25 · openalex publication_date 2005/10/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the homogenization of a Schrodinger equation in a periodic medium with a time dependent potential. This is a model for semiconductors excited by an external electromagnetic wave. We prove that, for a suitable choice of oscillating (both in time and space) potential, one can partially transfer electrons from one Bloch band to another. This justifies the famous "Fermi golden rule" for the transition probability between two such states which is at the basis of various optical properties of semiconductors. Our method is based on a combination of classical homogenization techniques (two-scale convergence and suitable oscillating test functions) and of Bloch waves theory.