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QCD vacuum as a disordered medium: a simplified model for the QCD dirac operator.

Antonio M García-García1, James C Osborn

  • 1Laboratoire de Physique Théorique et Modèles Statistiques, Bâtiment 100, Université de Paris-Sud, 91405 Orsay Cedex, France.

Physical Review Letters
|November 5, 2004
PubMed
Summary

We model the quantum chromodynamics (QCD) Dirac operator using a random banded matrix approach. This model shows spectral correlation agreement with the instanton liquid model, offering insights into QCD at finite temperatures.

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Area of Science:

  • Quantum Chromodynamics (QCD)
  • High Energy Physics
  • Condensed Matter Physics

Background:

  • The QCD Dirac operator describes the behavior of quarks in the strong nuclear force.
  • Understanding its spectral properties is crucial for comprehending QCD at finite temperatures.
  • Instanton liquid models (ILM) provide a framework for studying QCD vacuum properties.

Purpose of the Study:

  • To model the QCD Dirac operator using a power-law random banded matrix (RBM) with chiral symmetry.
  • To compare the spectral correlations of the RBM with those of an instanton liquid model (ILM).
  • To investigate the scaling behavior of the Thouless energy in different spectral regions.

Main Methods:

  • Modeling the QCD Dirac operator as a power-law random banded matrix (RBM).

Related Experiment Videos

  • Analyzing spectral correlations and Thouless energy scaling.
  • Comparing RBM results with an instanton liquid model (ILM) and chiral perturbation theory.

    • Main Results:

    • The RBM shows spectral correlation agreement with the ILM beyond the Thouless energy.
    • In the bulk spectrum, the RBM's dimensionless Thouless energy scales with system size, matching the ILM and chiral perturbation theory.
    • Near the origin, the RBM's scaling aligns with chiral perturbation theory but differs from the ILM.

    Conclusions:

    • The power-law random banded matrix model effectively captures key spectral correlation properties of the QCD Dirac operator.
    • The model's agreement with chiral perturbation theory, particularly near the origin, highlights its potential.
    • Further modifications to the RBM are needed to accurately describe spectral correlations at the finite temperature chiral restoration transition.