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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series B Année : 2006

Homogenization of the Schrodinger equation with a time oscillating potential

Résumé

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.
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Dates et versions

hal-00012604 , version 1 (25-10-2005)

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Grégoire Allaire, Muthusamy Vanninathan. Homogenization of the Schrodinger equation with a time oscillating potential. Discrete and Continuous Dynamical Systems - Series B, 2006, 6, pp.1-16. ⟨hal-00012604⟩
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