Time-dependent density-functional and reduced density-matrix methods for few electrons: Exact versus adiabatic approximations

N. Helbig*, J. I. Fuks, I. V. Tokatly, H. Appel, E. K.U. Gross, A. Rubio

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


To address the impact of electron correlations in the linear and non-linear response regimes of interacting many-electron systems exposed to time-dependent external fields, we study one-dimensional (1D) systems where the interacting problem is solved exactly by exploiting the mapping of the 1D N-electron problem onto an N-dimensional single electron problem. We analyze the performance of the recently derived 1D local density approximation as well as the exact-exchange orbital functional for those systems. We show that the interaction with an external resonant laser field shows Rabi oscillations which are detuned due to the lack of memory in adiabatic approximations. To investigate situations where static correlations play a role, we consider the time-evolution of the natural occupation numbers associated to the reduced one-body density matrix. Those studies shed light on the non-locality and time-dependence of the exchange and correlation functionals in time-dependent density and density-matrix functional theories.

Original languageAmerican English
Pages (from-to)1-10
Number of pages10
JournalChemical Physics
Issue number1
StatePublished - 24 Nov 2011
Externally publishedYes

Bibliographical note

Funding Information:
The authors thank Michele Casula, Matthieu Verstraete, Miguel Marques, and Xavier Andrade for helpful discussions. We acknowledge support by MICINN (FIS2010-21282-C02-01), ACI-promociona (ACI2009-1036), “Grupos Consolidados UPV/EHU del Gobierno Vasco” (IT-319-07), and the European Community through e-I3 ETSF project (Contract No. 211956).


  • Adiabatic functionals
  • One-body density matrix
  • Solvable model systems
  • Time-dependent density-functional theory


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