# Second-order homogenization of periodic Schr\"odinger operators with highly oscillating potentials

@inproceedings{Cances2021SecondorderHO, title={Second-order homogenization of periodic Schr\"odinger operators with highly oscillating potentials}, author={'Eric Cances and Louis Garrigue and David Gontier}, year={2021} }

We consider the homogenization at second-order in ε of Lperiodic Schrödinger operators with rapidly oscillating potentials of the form H = −∆+ε−1v(x, ε−1x)+W (x) on L(R), where L is a Bravais lattice of R, v is (L × L)-periodic, W is L-periodic, and ε ∈ N−1. We treat both the linear equation with fixed right-hand side and the eigenvalue problem, as well as the case of physical observables such as the integrated density of states. We illustrate numerically that these corrections to the…

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