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Volume 35, Issue 4
Localization in the Incommensurate Systems: A Plane Wave Study via Effective Potentials

Ting Wang, Yuzhi Zhou & Aihui Zhou

DOI: 10.4208/cicp.OA-2023-0203

Commun. Comput. Phys., 35 (2024), pp. 1029-1044.

Published online: 2024-05

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  • Abstract

In this paper, we apply the effective potentials in the localization landscape theory (Filoche et al., 2012, Arnold et al., 2016) to study the spectral properties of the incommensurate systems. We uniquely develop a plane wave framework for the effective potentials of the incommensurate systems. And utilizing the effective potentials represented by the plane wave, the location of the electron density can be inferred. Moreover, the spectral distribution can be obtained from the effective potential version of Weyl’s law. We perform some numerical experiments on some typical incommensurate systems, showing that the effective potential provides an alternative tool for investigating the localization and spectral properties of the incommensurate systems, without solving the eigenvalue problem explicitly.

  • Keywords

Incommensurate systems, localization, effective potential, plane wave method.

  • AMS Subject Headings

35J10, 35P15, 35Q40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-35-1029, author = {Wang , TingZhou , Yuzhi and Zhou , Aihui}, title = {Localization in the Incommensurate Systems: A Plane Wave Study via Effective Potentials}, journal = {Communications in Computational Physics}, year = {2024}, volume = {35}, number = {4}, pages = {1029--1044}, abstract = {

In this paper, we apply the effective potentials in the localization landscape theory (Filoche et al., 2012, Arnold et al., 2016) to study the spectral properties of the incommensurate systems. We uniquely develop a plane wave framework for the effective potentials of the incommensurate systems. And utilizing the effective potentials represented by the plane wave, the location of the electron density can be inferred. Moreover, the spectral distribution can be obtained from the effective potential version of Weyl’s law. We perform some numerical experiments on some typical incommensurate systems, showing that the effective potential provides an alternative tool for investigating the localization and spectral properties of the incommensurate systems, without solving the eigenvalue problem explicitly.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0203}, url = {http://global-sci.org/intro/article_detail/cicp/23093.html} }
TY - JOUR T1 - Localization in the Incommensurate Systems: A Plane Wave Study via Effective Potentials AU - Wang , Ting AU - Zhou , Yuzhi AU - Zhou , Aihui JO - Communications in Computational Physics VL - 4 SP - 1029 EP - 1044 PY - 2024 DA - 2024/05 SN - 35 DO - http://doi.org/10.4208/cicp.OA-2023-0203 UR - https://global-sci.org/intro/article_detail/cicp/23093.html KW - Incommensurate systems, localization, effective potential, plane wave method. AB -

In this paper, we apply the effective potentials in the localization landscape theory (Filoche et al., 2012, Arnold et al., 2016) to study the spectral properties of the incommensurate systems. We uniquely develop a plane wave framework for the effective potentials of the incommensurate systems. And utilizing the effective potentials represented by the plane wave, the location of the electron density can be inferred. Moreover, the spectral distribution can be obtained from the effective potential version of Weyl’s law. We perform some numerical experiments on some typical incommensurate systems, showing that the effective potential provides an alternative tool for investigating the localization and spectral properties of the incommensurate systems, without solving the eigenvalue problem explicitly.

Ting Wang, Yuzhi Zhou & Aihui Zhou. (2024). Localization in the Incommensurate Systems: A Plane Wave Study via Effective Potentials. Communications in Computational Physics. 35 (4). 1029-1044. doi:10.4208/cicp.OA-2023-0203
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