Share This Article:

On the Validity of Janak’s Theorem and Ground State Energies of Ensembles of Interacting Quantum N-Particle Systems

Abstract Full-Text HTML Download Download as PDF (Size:273KB) PP. 78-83
DOI: 10.4236/wjcmp.2014.42012    3,014 Downloads   4,149 Views   Citations
Author(s)    Leave a comment

ABSTRACT

It is established that for finite number of electrons, N < , and in the limit T = 0, the line of reasoning leading to the proof of Janak’s theorem is flawed, based on the incorrect treatment of a mixed state as a pure state. The derivative discontinuity at integral values of N of the total ground state energy, Ev[N], of an interacting N-particle system under an external single-particle potential, v(r), is shown to follow from general quantum principles governing the behavior of ensembles of systems with varying particle number, and its presence is shown to be independent of the particular approximation used in determining the total ground-state energy of an ensemble.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Gonis, A. (2014) On the Validity of Janak’s Theorem and Ground State Energies of Ensembles of Interacting Quantum N-Particle Systems. World Journal of Condensed Matter Physics, 4, 78-83. doi: 10.4236/wjcmp.2014.42012.

References

[1] Janak, J.F. (1978) Proof That in Density-Functional Theory. Physical Review B, 18, 7165-7168.
http://dx.doi.org/10.1103/PhysRevB.18.7165
[2] Perdew, J.P., Parr, R.G., Levy, M. and Balduz, J.L. (1982) Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy. Physical Review Letters, 49, 1691-1694.
http://dx.doi.org/10.1103/PhysRevLett.49.1691
[3] Perdew, J.P. and Levy, M. (1983) Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities. Physical Review Letters, 51, 1884-1887.
http://dx.doi.org/10.1103/PhysRevLett.51.1884
[4] Zheng, X., Cohen, A.J., Mori-Sánchez, P., Hu, X.Q. and Yang, W. (2011) Improving Band Gap Prediction in Density Functional Theory from Molecules to Solids. Physical Review Letters, 107, Article ID: 026403.
http://dx.doi.org/10.1103/PhysRevLett.51.1884
[5] Goransson, C., Olovsson, W. and Abrikosov, I.A. (2005) Numerical Investigation of the Validity of the Slater-Janak Transition-State Model in Metallic Systems. Physical Review B, 72, Article ID: 134203.
http://dx.doi.org/10.1103/PhysRevB.72.134203
[6] Sanna, S., Frauenheim, T. and Gerstmann, U. (2008) Validity of the Slater-Janak Transition-State Model within the Approach. Physical Review B, 78, Article ID: 085201.
http://dx.doi.org/10.1103/PhysRevB.78.085201
[7] Elkind, P.D. and Staroverov, V.N. (2012) Energy Expressions for Kohn-Sham Potentials and Their Relation to the Slater-Janak Theorem. The Journal of Chemical Physics, 136, Article ID: 124115.
http://dx.doi.org/10.1063/1.3695372
[8] Chakrabarty, A. and Patterson, C.H. (2012) Transition Levels of Defects in Zno: Total Energy and Janak’s Theorem Methods. The Journal of Chemical Physics, 137, Article ID: 054709.
http://dx.doi.org/10.1063/1.4739316
[9] Hohenberg, P. and Kohn, W. (1964) Inhomogeneous Electron Gas. Physical Review, 136, B864-B871.
http://dx.doi.org/10.1103/PhysRev.136.B864
[10] Kohn, W. and Sham, L.J. (1965) Self-Consistent Equations Including Exchange and Correlation Effects. Physical Review, 140, A1133-A1138. http://dx.doi.org/10.1103/PhysRev.140.A1133
[11] Slater, J.C. (1972) Statistical Exchange-Correlation in the Self-Consistent Field. Volume 6 of Advances in Quantum Chemistry, Academic Press, 1-92.
[12] Pitaevskii, L.P. and Lifshitz, E.M. (1981) Statistical Physics. Part 2. Butterworth-Heinemann, Oxford.
[13] Gorkov, A.A., Dzyaloshinskii, L.P. and Abrikosov, I.Y. (1965) Quantum Field Theoretical Methods in Statistical Physics. Pergamon Press, New York.
[14] Phillips, P. (2008) Advanced Solid State Physics. Perseus Books.
[15] Monkhorst, H.J., Harris, F.E. and Freeman, F.E. (1992) Algebraic and Diagrammatic Methods in Many-Fermion Theory. Oxford University Press, Oxford.
[16] http://www.pma.caltech.edu/mcc/Ph127/c/Lecture9.pdf

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.