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Current-Density Functional Theory of Linear Response to Time-Dependent Electromagnetic Fields

  • G. Vignale
  • Walter Kohn

Abstract

Local density approximations are known to be very useful in calculating the ground-state exchange and correlation (xc) energy of many-electron systems [1], and local approximations are gaining in importance for the description of xc effects in time-dependent situations also [2,3]. Most of the time-dependent work has dealt with a scalar time-dependent xc potential \({v_{xc}}(\vec r,\omega )\) approximated as a local functional of the time-dependent density \(n(\vec r,\omega )\) as described in the chapter “Time-dependent density functional theory” in the introductory section of this Book. Despite much progress in this scalar approach, it will be shown in this Chapter that existing approximations for v xc require modification. In particular, it will be shown that (i) there is no local density approximation for the scalar xc potential at finite frequency (ii) there is, however, a consistent local approximation for a vector xc potential \({{\vec a}_{xc}}(\vec r,\omega )\) in terms of the dynamic current density \(\vec j(\vec r,\omega )\) and its space derivatives, as well as the ground-state density and its space derivatives. This approximation is valid, at a given frequency, for sufficiently slow spatial variations of the ground-state density and of the perturbing dynamic potential. The appropriately modified vector xc potential will be derived here in some detail, thus filling out the brief description published recently [4]. New material will also be presented, providing interpretation of the findings in the simple case of one dimensional inhomogeneity.

Keywords

Local Density Approximation Time Dependent Density Functional Theory Gradient Expansion Accelerate Frame Local Field Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    W. Kohn and L. Sham, Phys. Rev. 140, A1133 (1965).MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    E. K. U. Gross and W. Kohn, Phys. Rev. Lett. 55, 2850 (1985).ADSCrossRefGoogle Scholar
  3. E. K. U. Gross and W. Kohn, Adv. Quantum Chemistry 21, 255 (1990).ADSCrossRefGoogle Scholar
  4. 3.
    A. Zangwill and P. Soven Phys. Rev. Lett. 45, 204 (1980); Phys. Rev. B 24, 4121 (1981).ADSCrossRefGoogle Scholar
  5. 4.
    G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996).ADSCrossRefGoogle Scholar
  6. 5.
    E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997, (1984).ADSCrossRefGoogle Scholar
  7. 6.
    In this paper, a function \(f(\vec r\, - \,\vec r)\) is said to be of short range if the integral \(\int {f(\vec r,\,\vec r\, + \vec s)} d\vec s\) is finite. This is equivalent to saying that the Fourier transform of f, with wave vector →k, with respect to the separation \(\vec s\, = \,\vec r\, - \,\vec r\), remains finite in the limit \(\vec k \to 0.\).Google Scholar
  8. 7.
    H.M. Böhm, S. Conti, and M. P. Tosi, J. Phys.: Condensed Matter 8, 781 (1996).ADSCrossRefGoogle Scholar
  9. 8.
    J. F. Dobson, Phys. Rev. Lett. 73, 2244 (1994).ADSCrossRefGoogle Scholar
  10. 9.
    W. Kohn, Phys. Rev. 123, 1242 (1961), L. Brey et al, Phys. Rev. B 40, 10647 (1989); ibid. 42, 1240 (1990); S. K. Yip, Phys. Rev. B 43, 1707 (1991).ADSzbMATHCrossRefGoogle Scholar
  11. 10.
    J. F. Dobson, M. Bünner, and E. K. U. Gross, Phys. Rev. Lett. 79, 1905 (1997).ADSCrossRefGoogle Scholar
  12. 11.
    J. F. Dobson, Proceedings of the NATO ASI on Density Functional Theory, edited by E. K. U. Gross and R. M. Dreizler (Plenum, New York, 1994), p. 393.Google Scholar
  13. 12.
    G. Vignale, Phys. Rev. Lett. 74, 3233 (1995).ADSCrossRefGoogle Scholar
  14. 13.
    G. Vignale, Phys. Lett. A 209, 206 (1995).ADSCrossRefGoogle Scholar
  15. 14.
    P. Nozières, The Theory of Interacting Fermi Systems (W. A. Benjamin, New York, 1964), Chapter 6.Google Scholar
  16. 15.
    Tai Kai Ng, Phys. Rev. Lett. 62, 2417 (1989).ADSCrossRefGoogle Scholar
  17. 16.
    K. S. Singwi and M. P. Tosi, in Solid State Physics, edited by H. Ehrenreich, F. Scitz, and D. Turnbull (Academic, New York, 1981), Vol. 36, p. 177.Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • G. Vignale
    • 1
  • Walter Kohn
    • 2
  1. 1.Department of PhysicsUniversity of MissouriColumbiaUSA
  2. 2.Department of PhysicsUniversity of CaliforniaSanta BarbaraUSA

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