A stochastic method to compute the $L^2$ localisation landscape
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866910397500489728 |
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| author | Kakoi, Masataka Slevin, Keith |
| author_facet | Kakoi, Masataka Slevin, Keith |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_10768 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A stochastic method to compute the $L^2$ localisation landscape Kakoi, Masataka Slevin, Keith Disordered Systems and Neural Networks 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. |
| title | A stochastic method to compute the $L^2$ localisation landscape |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2212.10768 |