Advertisement

A Density Functional Formalism for Condensed Matter Systems

  • A. K. Rajagopal
Part of the NATO ASI Series book series (volume 123)

Abstract

A very large part of research in condensed matter physics may be considered as investigations of inhomogeneous electron systems. The inhomogeneities are due to nuclear charges located in certain geometrical forms (single nuclear charge for an atom, a small number of several nuclear charges distributed spatially to form small molecules, or a large number of nuclei arranged in a regular spatial three-dimensional array to form a solid etc.). We will not be interested here in amorphous systems even though a density functional scheme is being used in the liquid state research. Also we will not be interested in the detailed properties of the nuclei themselves and treat them as merely positively charged entities with no intrinsic character to them. One class of questions concerns the electronic properties including its spin effects and our main attention will be focussed on these. There have been some attempts to examine nuclear motions (molecular vibrations and phonons in solids) using density functional formalism; but this has not yet been explored fully as will be pointed out later. The central theme in the original density-functional formalism was that the ground state (equilibrium) properties depend only on the ground state (equilibrium) density of the electrons and the nuclei. Stated in this way, we may think of these problems as another facet of Relativistic Quantum Electrodynamics of many electrons and structureless charge compensating nuclei, which for all practical purposes can be treated as classical objects.

Keywords

Finite Temperature Nuclear Charge Grand Canonical Ensemble Nuclear Motion Dirac Field 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. S. Fradkin, Proc. (Trudy) Lebedev Phys. Inst. 29, 1 (1967).Google Scholar
  2. 2.
    B. Bezzerides and D. F. Dubois, Ann. Phys. (N.Y.) 70, 10 (1972).ADSCrossRefGoogle Scholar
  3. 3.
    R. L. Bowers, J. A. Campbell, and R. L. Zimmerman, Phys. Rev. D 7, 2278 (1973).ADSCrossRefGoogle Scholar
  4. 4.
    C. W. Bernard, Phys. Rev. D 9, 3312 (1974).ADSGoogle Scholar
  5. 5.
    L. Dolan and R. Jackiw, Phys. Rev. D 9, 3320 (1974).ADSCrossRefGoogle Scholar
  6. 6.
    S. Weinberg, Phys. Rev. D 9, 3357 (1974).ADSCrossRefGoogle Scholar
  7. 7.
    S. A. Chin, Ann. Phys. (N.Y.) 108, 301 (1977).ADSCrossRefGoogle Scholar
  8. 8.
    A. Bechler, Ann. Phys. (N.Y.) 135, 19 (1981). This paper gives references to many other studies on relativistic many-body theory of matter at high densities and temperatures relevant to astrophysical phenomena and nuclear matter.Google Scholar
  9. 9.
    A. K. Rajagopal, Adv. in Chem. Phys. 41, 59 (1980).Google Scholar
  10. 10.
    U. Gupta and A. K. Rajagopal, Phys. Rev. C 87, 259 (1982).Google Scholar
  11. 11.
    M. V. Ramana and A. K. Rajagopal, Adv. in Chem. Phys. 54, 231 (1983).Google Scholar
  12. 12.
    W. Kohn and P. Vashishta, review article in Physics of Solids and Liquids, (eds. S. Lundqvist and N. H. March) Plenum Press (to appear, 1983 ).Google Scholar
  13. 13.
    J. Callaway and N. H. March, review article in Advances in Solid State Physics, (eds. H. Ehrenreich, F. Seitz, and D. Turnbull) Academic Press (N.Y.) (to appear, 1983 ).Google Scholar
  14. 14.
    A. R. Williams and U. von Barth, review article in Physics of Solids and Liquids, (eds. S. Lundqvist and N. H. March) Plenum Press (to appear, 1983 ).Google Scholar
  15. 15.
    M. Levy, Proc. Natl. Acad. Sci. (USA) 76, 6062 (1979) and M. Levy, Phys. Rev. A 26, 1200 (1982).CrossRefGoogle Scholar
  16. 16.
    E. H. Lieb, in Physics as Natural Philosophy, (ed. by A. Shimony and H. Feshbach ), MIT Press, Cambridge, Mass., (1982).Google Scholar
  17. 17.
    M. W. C. Dharma-wardana and F. Perrot, Phys. Rev. A 26, 2096 (1982).ADSCrossRefGoogle Scholar
  18. 18.
    M. W. C. Dharma-wardana, F. Perrot, and G. C. Aers, Phys. Rev. A 28, 344 (1983).ADSCrossRefGoogle Scholar
  19. 19.
    J. Capitani, R. F. Nalewajski, and R. G. Parr, J. Chem. Phys. 76, 568 (1982).ADSCrossRefGoogle Scholar
  20. 20.
    M. P. Das, M. V. Ramana, and A. K. Rajagopal, Phys. Rev. A 22, 9 (1980).ADSCrossRefGoogle Scholar
  21. 21.
    F. Perrot, Phys. Rev. A 25, 489 (1982).ADSCrossRefGoogle Scholar
  22. 22.
    F. Perrot, Phys. Rev. A 26, 1035 (1982).ADSCrossRefGoogle Scholar
  23. 23.
    U. Gupta and A. K. Rajagopal, J. Phys. B: Atomic and Mol. Phys. 12, 2703 (1979); 14, 2309 (1981).CrossRefGoogle Scholar
  24. 24.
    U. Gupta and A. K. Rajagopal, Phys. Rev. A 21, 2064 (1980) and A 22, 2792 (1980).ADSCrossRefGoogle Scholar
  25. 25.
    U. von Barth, review article in the Nato Advanced Study Institute held in Gent, July 1982.Google Scholar
  26. 26.
    F. A. Parpia and W. R. Johnson, J. Phys. B: At. and Mol. Phys. 16, L375 (1983), and private communication (1983).Google Scholar
  27. 27.
    Ann-Marie Martensson, Physica Scripta 21, 293 (1980).ADSCrossRefGoogle Scholar
  28. 28.
    D. D. Koelling and A. H. MacDonald, review article in the Nato Summer School Lectures, Burnaby B.C., Summer (1981).Google Scholar
  29. 29.
    N. D. Lang, review article in Physics of Solids and Liquids, (eds. S. Lundqvist and N. H. March) Plenum Press, (to appear, 1983 ).Google Scholar
  30. 30.
    R. Colle and O. Salvetti, J. Chem. Phys. 79, 1404 (1983).ADSGoogle Scholar
  31. 31.
    J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, Jr., Phys. Rev. Lett. 49, 1691 (1982).ADSCrossRefGoogle Scholar
  32. 32.
    R. A. Harris and J. A. Cina, J. Chem. Phys. 79, 1381 (1983).ADSCrossRefGoogle Scholar
  33. 33.
    A. H. MacDonald, J. Phys. C: Solid State Phys. 16, 3869 (1983).ADSCrossRefGoogle Scholar
  34. 34.
    Bu-Xing Xu, A. K. Rajagopal, and M. V. Ramana, J. Phys. C: Solid State Phys. (to appear, 1983 ).Google Scholar
  35. 35.
    G. E. Bauer, Phys. Rev. B 27, 5912 (1983).ADSCrossRefGoogle Scholar
  36. 36.
    G. Zumbach and K. Maschke, Phys. Rev. A 28, 544 (1983).MathSciNetADSCrossRefGoogle Scholar
  37. 37.
    A. K. Rajagopal, unpublished notes (1983).Google Scholar

Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • A. K. Rajagopal
    • 1
  1. 1.Department of Physics and AstronomyLouisiana State UniversityBaton RougeUSA

Personalised recommendations