Reverse engineering in many-body quantum physics: Correspondence between many-body systems and effective single-particle equations

J. P. Coe, K. Capelle, and I. D’Amico
Phys. Rev. A 79, 032504 – Published 5 March 2009

Abstract

The mapping, exact or approximate, of a many-body problem onto an effective single-body problem is one of the most widely used conceptual and computational tools of physics. Here, we propose and investigate the inverse map of effective approximate single-particle equations onto the corresponding many-particle system. This approach allows us to understand which interacting system a given single-particle approximation is actually describing, and how far this is from the original physical many-body system. We illustrate the resulting reverse engineering process by means of the Kohn-Sham equations of density-functional theory. In this application, our procedure sheds light on the nonlocality of the density-potential mapping of density-functional theory, and on the self-interaction error inherent in approximate density functionals.

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  • Received 1 September 2008

DOI:https://doi.org/10.1103/PhysRevA.79.032504

©2009 American Physical Society

Authors & Affiliations

J. P. Coe1,2,*, K. Capelle3,4, and I. D’Amico1,†

  • 1Department of Physics, University of York, York YO10 5DD, United Kingdom
  • 2Department of Mathematics, University of York, York YO10 5DD, United Kingdom
  • 3Departamento de Física e Informática, Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, SP, Brazil
  • 4Theoretische Physik, Freie Universität Berlin, D-14195 Berlin, Germany

  • *jpc503@york.ac.uk
  • ida500@york.ac.uk

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Issue

Vol. 79, Iss. 3 — March 2009

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