Landscape-Theory

Findings by M. L. Lyra, S. Mayboroda and M. Filoche relate invertibility and positivity of a class of discrete Schrodinger matrices with the existence of the “Landscape Function,” which provides an upper bound on all eigenvectors simultaneously. Their argument is based on the variational principles. We consider an alternative method of proving these results, based on the power series expansion of matrices, and demonstrate that it naturally extends the original findings to the case of long range operators.