1 November 2023 Wed 4 pm

The L2 localisation landscape of L. Herviou and J. H. Bardarson [1] is a generalisation of the localisation landscape of M. Filoche and S. Mayboroda [2]. In [3] we proposed a stochastic method to compute the L2 localisation landscape that enables the calculation of landscapes using sparse matrix methods. We also proposed 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 demonstrated the utility of these suggestions by applying the L2 landscape to Anderson’s model of localisation in one and two dimensions, and to localisation in a model of the quantum Hall effect. 1. Herviou, L. and J.H. Bardarson, L2 localization landscape for highly excited states. Physical Review B, 2020. 101(22): p. 220201. 2. Filoche, M. and S. Mayboroda, Universal mechanism for Anderson and weak localization. Proceedings of the National Academy of Sciences, 2012. 109(37): p. 14761-14766. 3. Kakoi, M. and K. Slevin, A Stochastic Method to Compute the L2 Localisation Landscape. Journal of the Physical Society of Japan, 2023. 92(5): p. 054707.

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