Numerical construction of the density-potential mapping

Soeren E. B. Nielsen (), Michael Ruggenthaler and Robert van Leeuwen
Additional contact information
Soeren E. B. Nielsen: Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science
Michael Ruggenthaler: Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science
Robert van Leeuwen: Nanoscience Center, University of Jyväskylä

The European Physical Journal B: Condensed Matter and Complex Systems, 2018, vol. 91, issue 10, 1-19

Abstract: Abstract We demonstrate how a recently developed method Nielsen et al. [Nielsen et al., EPL 101, 33001 (2013)] allows for a comprehensive investigation of time-dependent density functionals in general, and of the exact time-dependent exchange-correlation potential in particular, by presenting the first exact results for two- and three-dimensional multi-electron systems. This method is an explicit realization of the Runge–Gross correspondence, which maps time-dependent densities to their respective potentials, and allows for the exact construction of desired density functionals. We present in detail the numerical requirements that makes this method efficient, stable and precise even for large and rapid density changes, irrespective of the initial state and two-body interaction. This includes among others the proper treatment of low density regions, a subtle interplay between numerical time-propagation and zero boundary conditions, the choice of time-stepping strategy, and an error damping mechanism based on both the density and current density residuals. These considerations are also relevant for computing time-independent density-functionals and lead to a more precise implementation of quantum mechanics in general, which is mainly relevant for cases in which there is notable contact with a boundary or when the low density regions matter.

Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1140/epjb/e2018-90276-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:91:y:2018:i:10:d:10.1140_epjb_e2018-90276-4

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/e2018-90276-4

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().