• Corpus ID: 245385798

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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