Finite-size effects in response functions of molecular systems
The SMAI Journal of computational mathematics, Volume 8 (2022), pp. 273-294.

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.

Published online:
DOI: 10.5802/smai-jcm.87
Classification: 35P25, 35Q40
Keywords: linear response, scattering, limiting absorption principle, finite-size effects
Mi-Song Dupuy 1; Antoine Levitt 2

1 Laboratoire Jacques-Louis Lions, Sorbonne Université, Paris, France
2 Inria Paris and Université Paris-Est, CERMICS, École des Ponts ParisTech, Marne-la-Vallée, France
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Mi-Song Dupuy; Antoine Levitt. Finite-size effects in response functions of molecular systems. The SMAI Journal of computational mathematics, Volume 8 (2022), pp. 273-294. doi : 10.5802/smai-jcm.87. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.87/

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