We consider an electron in a localized potential submitted to a weak external, time-dependent field. In the linear response regime, the response function can be computed using Kubo’s formula. In this paper, we consider the numerical approximation of the response function by means of a truncation to a finite region of space. This is necessarily a singular approximation because of the discreteness of the spectrum of the truncated Hamiltonian, and in practice a regularization (smoothing) has to be used. Our results provide error estimates for the response function past the ionization threshold with respect to both the smoothing parameter and the size of the computational domain.
Mots clés : linear response, scattering, limiting absorption principle, finite-size effects
@article{SMAI-JCM_2022__8__273_0,
author = {Dupuy, Mi-Song and Levitt, Antoine},
title = {Finite-size effects in response functions of molecular systems},
journal = {The SMAI Journal of computational mathematics},
pages = {273--294},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {8},
year = {2022},
doi = {10.5802/smai-jcm.87},
language = {en},
url = {http://www.numdam.org/articles/10.5802/smai-jcm.87/}
}
TY - JOUR AU - Dupuy, Mi-Song AU - Levitt, Antoine TI - Finite-size effects in response functions of molecular systems JO - The SMAI Journal of computational mathematics PY - 2022 SP - 273 EP - 294 VL - 8 PB - Société de Mathématiques Appliquées et Industrielles UR - http://www.numdam.org/articles/10.5802/smai-jcm.87/ DO - 10.5802/smai-jcm.87 LA - en ID - SMAI-JCM_2022__8__273_0 ER -
%0 Journal Article %A Dupuy, Mi-Song %A Levitt, Antoine %T Finite-size effects in response functions of molecular systems %J The SMAI Journal of computational mathematics %D 2022 %P 273-294 %V 8 %I Société de Mathématiques Appliquées et Industrielles %U http://www.numdam.org/articles/10.5802/smai-jcm.87/ %R 10.5802/smai-jcm.87 %G en %F SMAI-JCM_2022__8__273_0
Dupuy, Mi-Song; Levitt, Antoine. Finite-size effects in response functions of molecular systems. The SMAI Journal of computational mathematics, Tome 8 (2022), pp. 273-294. doi : 10.5802/smai-jcm.87. http://www.numdam.org/articles/10.5802/smai-jcm.87/
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