Nonexistence of a Taylor expansion in time due to cusps

Zeng-hui Yang and Kieron Burke
Phys. Rev. A 88, 042514 – Published 25 October 2013

Abstract

In the usual treatment of electronic structure, all matter has cusps in the electronic density at nuclei. Cusps can produce nonanalytic behavior in time, even in response to perturbations that are time analytic. We analyze these nonanalyticities in a simple case from many perspectives. We describe a method, the s expansion, that can be used in several such cases and illustrate it with a variety of examples. These include both the sudden appearance of electric fields and disappearance of nuclei in both one and three dimensions. When successful, the s expansion yields the dominant short-time behavior, no matter how strong the external electric field, but agrees with linear-response theory in the weak limit. We discuss the relevance of these results to time-dependent density functional theory.

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  • Received 21 August 2013

DOI:https://doi.org/10.1103/PhysRevA.88.042514

©2013 American Physical Society

Authors & Affiliations

Zeng-hui Yang

  • Department of Physics and Astronomy, University of Missouri-Columbia, Columbia, Missouri 65211, USA

Kieron Burke

  • Department of Chemistry, University of California-Irvine, Irvine, California 92697, USA

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Issue

Vol. 88, Iss. 4 — October 2013

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