Homogenization limits and Wigner transforms

摘要: We present a theory for carrying out homogenization limits quadratic functions (called “energy densities”) of solutions initial value problems (IVPs) with anti-self-adjoint (spatial) pseudo-differential operators (PDOs). The approach is based on the introduction phase space Wigner (matrix) measures that are calculated by solving kinetic equations involving spectral properties PDO. weak energy densities then obtained taking moments measure. The very general illustrated typical examples like (semi)classical Schrodinger (with or without periodic potential), limit acoustic equation in medium, and classical Dirac equation. © 1997 John Wiley & Sons, Inc.