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# Homogenization of Schrödinger equation with a large periodic potential

GFM seminar
CIUL, B3-01
2006-03-03 14:30 .. 15:30
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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.