A stochastic method to compute the $L^2$ localisation landscape

Abstract

The $L^2$ 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 $L^2$ localisation landscape that enables the calculation of landscapes using sparse matrix methods. We also propose an energy filtering of the $L^2$ 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 $L^2$ landscape to Anderson's model of localisation in one and two dimensions, and also to localisation in a model of the quantum Hall effect.

9 pages, 6 figures

References in corpus (4)

• The Kernel Polynomial Method
• ${\mathcal{L}}^2$ localization landscape for highly-excited states
• Wigner-Weyl description of light absorption in disordered semiconductor alloys using the localization landscape theory
• Spectral functions and localization landscape theory in speckle potentials