Landscape approach of localisation

In 2012, Filoche and Mayboroda have proposed a new picture on Anderson localisation, based on a bound of the wave function (M. Filoche and S. Mayboroda, Proc. Nat. Acad. Sci. U.S.A. 109(37), 14761–14766 (2012)). As an application, they have proposed a formula for estimating the DoS of disordered Schrödinger Hamiltonians (D. N. Arnold, G. David, D. Jerison, S. Mayboroda, and M. Filoche, Phys. Rev. Lett. 116, 056602 (2016)). Only simple numerical tests were presented in this reference. In the following short note, we provide the first analytical tests on specific models and show that the landscape estimation fails to predict the details of the spectral singularities:

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