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The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

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Atomic Nuclei: Nuclear Spin State Population Distribution01:14

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Related Experiment Video

Updated: Jun 17, 2026

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
09:00

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Published on: June 28, 2018

Interacting electrons, spin statistics, and information theory.

L M Ghiringhelli1, I P Hamilton, L Delle Site

  • 1Max-Planck-Institut für Polymerforschung, Ackermannweg 10, D-55128 Mainz, Germany. luca@fhi-berlin.mpg.de

The Journal of Chemical Physics
|January 19, 2010
PubMed
Summary
This summary is machine-generated.

Incorporating electron spin statistics into a kinetic energy functional approximation improves its accuracy. This method, using Shannon entropy, now satisfies the rigorous Lieb-Thirring inequality for interacting electron gases.

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Area of Science:

  • Quantum mechanics
  • Computational physics
  • Information theory

Background:

  • A prior method approximated electron kinetic energy functionals using Shannon entropy.
  • This previous approach failed to satisfy the Lieb-Thirring inequality for spinless electrons.

Purpose of the Study:

  • To develop an improved kinetic energy functional for interacting electron gases.
  • To ensure the functional satisfies fundamental physical inequalities, specifically the Lieb-Thirring inequality.

Main Methods:

  • Extension of the Levy-Lieb constrained search principle.
  • Monte Carlo sampling of electron configurations.
  • Inclusion of fermionic spin statistics via a statistical spin approach.

Main Results:

  • The refined procedure yields correlation terms also in the form of Shannon entropy.
  • The resulting kinetic energy functional now satisfies the Lieb-Thirring inequality.
  • This validates the connection between Shannon entropy and electron correlation.

Conclusions:

  • Fermionic spin statistics are crucial for accurate kinetic energy functionals.
  • The study strengthens the link between information theory (Shannon entropy) and quantum mechanics.
  • The developed method provides a more rigorous theoretical framework for electron systems.