Homogenization of Schrödinger equation with a large periodic potential
by Andrey Piatnitski (Narvik Univ. College, Norway and Lebedev Physical Inst. RAS, Moscow, Russia)
The talk will focus on homogenization of a Schroedinger equation with a large periodic rapidly oscillating potential.
We obtain a rigorous derivation of the so-called effective mass theorems in solid state physics. More precisely, for well-prepared initial data concentrating on a Bloch eigenfunction we prove that the solution can be asymptotically represented as the product of a fast oscillating Bloch eigenfunction and a slowly varying solution of a homogenized Schroedinger equation. The homogenized coefficients depend on the chosen Bloch eigenvalue, and the homogenized solution may experience a large drift. For the corresponding stationary Schroedinger equation the asymptotics of the bottom of spectrum will be studied.