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Frontiers and Challenges in Warm Dense Matter pp 1–23Cite as

Time-Dependent Density-Functional Theory: Features and Challenges, with a Special View on Matter Under Extreme Conditions

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 96))

Abstract

Time-dependent density-functional theory (TDDFT) is a universal quantum mechanical approach to the dynamical many-body problem which can be used to describe matter that is driven out of equilibrium by arbitrary time-dependent perturbations. TDDFT is often applied in the linear-response regime to obtain information about electronic excitations and spectral properties, but it also holds in the strongly nonlinear regime, where the perturbations compete with or even override the internal interactions that provide the structure and stability of matter. The purpose of this article is to give a brief overview of the basic formalism of TDDFT, and then to discuss the advantages, successes, and challenges of TDDFT for describing matter under extreme conditions of pressure and external fields. Two questions will be particularly emphasized: what are “easy” and what are “tough” problems for TDDFT (both from a fundamental and practical point of view), and how can TDDFT deal with dissipation? Some answers will be given, and needs and directions for future research will be pointed out.

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Notes

  1. 1.

    Other discussions at this IPAM workshop on warm dense matter involved thermal DFT [1], which is rooted in equilibrium quantum statistical mechanics, and hence is used for static systems at high temperature and pressure. At present, no rigorous extension of thermal DFT to time-dependent and/or non-equilibrium systems exists.

  2. 2.

    We assume here that all Kohn-Sham orbitals are either fully occupied or empty. For simplicity, we disregard the possibility of fractional orbital occupation numbers, which would be associated with degeneracies.

  3. 3.

    The RPA in linear response is equivalent to the time-dependent Hartree approximation, and has no dynamical xc contributions. It is not to be confused with the RPA in ground-state DFT, which is a method to calculate correlation energies using the so-called adiabatic connection fluctuation-dissipation approach [22].

  4. 4.

    Note that \(\mathbf{j}(\mathbf{r},t)\) is the physical current density. This is in contrast with ground-state CDFT, where the basic variable is the paramagnetic current density [57, 58].

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Acknowledgements

This work was supported by NSF Grant No. DMR-1005651.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Missouri, Columbia, MO, 65211, USA

    Carsten A. Ullrich

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  1. Carsten A. Ullrich
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Correspondence to Carsten A. Ullrich .

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Editors and Affiliations

  1. Lawrence Livermore National Laboratory, Livermore, California, USA

    Frank Graziani

  2. Sandia National Laboratories, Albuquerque, New Mexico, USA

    Michael P. Desjarlais

  3. Institute of Physics, University of Rostock, Rostock, Germany

    Ronald Redmer

  4. Department of Physics, University of Florida, Gainesville, Florida, USA

    Samuel B. Trickey

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Ullrich, C.A. (2014). Time-Dependent Density-Functional Theory: Features and Challenges, with a Special View on Matter Under Extreme Conditions. In: Graziani, F., Desjarlais, M., Redmer, R., Trickey, S. (eds) Frontiers and Challenges in Warm Dense Matter. Lecture Notes in Computational Science and Engineering, vol 96. Springer, Cham. https://doi.org/10.1007/978-3-319-04912-0_1

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