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Journal of Chemical Physics / Volume 132 / Issue 1 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 132, 014106 (2010); http://dx.doi.org/10.1063/1.3280953 (8 pages)

Interacting electrons, spin statistics, and information theory

L. M. Ghiringhelli1, I. P. Hamilton2, and L. Delle Site1

1Max-Planck-Institut für Polymerforschung, Ackermannweg 10, D-55128 Mainz, Germany
2Department of Chemistry, Wilfrid Laurier University, Waterloo N2L 3C5, Canada

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(Received 21 July 2009; accepted 10 December 2009; published online 6 January 2010)

We consider a nearly (or quasi) uniform gas of interacting electrons for which spin statistics play a crucial role. A previously developed procedure, based on the extension of the Levy–Lieb constrained search principle and Monte Carlo sampling of electron configurations in space, allows us to approximate the form of the kinetic-energy functional. For a spinless electron gas, this procedure led to a correlation term, which had the form of the Shannon entropy, but the resulting kinetic-energy functional does not satisfy the Lieb–Thirring inequality, which is rigorous and one of the most general relations regarding the kinetic energy. In this paper, we show that when the fermionic character of the electrons is included via a statistical spin approach, our procedure leads to correlation terms, which also have the form of the Shannon entropy and the resulting kinetic-energy functional does satisfy the Lieb–Thirring inequality. In this way we further strengthen the connection between Shannon entropy and electron correlation and, more generally, between information theory and quantum mechanics.

© 2010 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. LEVY–LIEB CONSTRAINED SEARCH PRINCIPLE
  3. SPINLESS ELECTRON GAS
  4. STATISTICAL SPIN APPROACH: PAULI WEIGHTING FUNCTION
  5. MC EVALUATION
  6. RESULTS
  7. FISHER INFORMATION AND SHANNON ENTROPY
  8. CONCLUSIONS

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KEYWORDS and PACS

Keywords

electron correlations, electron gas, information theory, quantum theory, statistical analysis

PACS

  • 05.30.Fk

    Fermion systems and electron gas

  • 02.50.-r

    Probability theory, stochastic processes, and statistics

  • 03.65.-w

    Quantum mechanics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3280953

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    L. M. Ghiringhelli and L. Delle Site, Phys. Rev. B 77, 073104 (2008).

    A. Nagy, J. Chem. Phys. 119, 9401 (2003)JCPSA6000119000018009401000001.

    E. H. Lieb and W. Thirring, Phys. Rev. Lett. 35, 687 (1975).

    E. Romera and J. S. Dehesa, J. Chem. Phys. 120, 8906 (2004)JCPSA6000120000019008906000001.

    K. D. Sen, J. Antolín, and J. C. Angulo, Phys. Rev. A 76, 032502 (2007).

    P. W. Ayers, J. Math. Phys. 46, 062107 (2005)JMAPAQ000046000006062107000001.


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