Lr-CONVERGENCE OF A RANDOM SCHRÖDINGER TO A LINEAR BOLTZMANN EVOLUTION

We consider the quantum mechanical dynamics of an electron against a background lattice of impurity ions exhibiting randomly distributed interaction strengths. Models of this type (Anderson model) are widely used to investigate qualitative features of technically highly relevant classes of materials that comprise semiconductors. Questions of key mathematical interest, treated intensively in the literature, address the emergence of electric conduction and insulation. While there exist landmark mathematical results explaining disorder-induced insulation at strong coupling (Anderson localization, [1, 6]), the weak coupling regime is at present far less understood. In the latter context, we shall here analyze issues regarding the derivation of macroscopic transport equations. We study the macroscopic scaling and weak coupling limit of the quantum dynamics generated by the Hamiltonian