Semi-classical limit of a Schrödinger equation for a stratified material
The paper develops new methods to analyze semiclassical transport properties in stratified periodic structures, appropriate for solid state physics. The asymptotic behavior of the dynamics of electrons is investigated by a combination of Wigner transform and Bloch decomposition techniques. A semiclassical limit of solutions of the Schrödinger-Cauchy problem is found to be determined by solution of infinitely many transport (Vlasov) equations. This result is given in terms of limits of Wigner transforms, whose convergence is kept under control.
scientific article; zbMATH DE number 1463413