The L2 localisation landscape of L. Herviou and J. H. Bardarson is a generalisation of the localisation landscape of M. Filoche and S. Mayboroda. We propose a stochastic method to compute the L2 localisation landscape that enables the calculation of landscapes using sparse matrix methods. We also propose an energy filtering of the L2 landscape which can be used to focus on eigenstates with energies in any chosen range of the energy spectrum. We demonstrate the utility of these suggestions by applying the L2 landscape to Anderson's model of localisation in one and two dimensions, and also to localisation in a model of the quantum Hall effect.
Cite
@article{arxiv.2212.10768,
title = {A stochastic method to compute the $L^2$ localisation landscape},
author = {Masataka Kakoi and Keith Slevin},
journal= {arXiv preprint arXiv:2212.10768},
year = {2024}
}