scholarly journals Density profiles of small Dirac operator eigenvalues for two color QCD at nonzero chemical potential compared to matrix models

2005 ◽  
Vol 140 ◽  
pp. 568-570 ◽  
Author(s):  
Gernot Akemann ◽  
Elmar Bittner ◽  
Maria-Paola Lombardo ◽  
Harald Markum ◽  
Rainer Pullirsch
Keyword(s):  
Dirac Operator ◽  
Matrix Models ◽  
Chemical Potential ◽  
Density Profiles ◽  
Operator Eigenvalues

scholarly journals MATRIX MODELS AND QCD WITH CHEMICAL POTENTIAL

2007 ◽  
Vol 22 (06) ◽  
pp. 1077-1122 ◽  
Author(s):  
G. AKEMANN
Keyword(s):  
Dirac Operator ◽  
Matrix Models ◽  
Matrix Model ◽  
Chemical Potential ◽  
General Concept ◽  
Real Plane ◽  
Random Matrix Model ◽  
Symmetry Classes ◽  
Spectrum Matching ◽  
Model Approach

The random matrix model approach to quantum chromodynamics (QCD) with nonvanishing chemical potential is reviewed. The general concept using global symmetries is introduced, as well as its relation to field theory, the so-called epsilon regime of chiral perturbation theory (∊χPT). Two types of matrix model results are distinguished: phenomenological applications leading to phase diagrams, and an exact limit of the QCD Dirac operator spectrum matching with ∊χPT. All known analytic results for the spectrum of complex and symplectic matrix models with chemical potential are summarised for the symmetry classes of ordinary and adjoint QCD, respectively. These include correlation functions of Dirac operator eigenvalues in the complex plane for real chemical potential, and in the real plane for imaginary isospin chemical potential. Comparisons of these predictions to recent lattice simulations are also discussed.

Quantum chromodynamics

2018 ◽  
Author(s):  
Marcos Marino
Keyword(s):  
Symmetry Breaking ◽  
Dirac Operator ◽  
Global Symmetries ◽  
Quantum Chromodynamics ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Matrix Theory ◽  
Global Symmetry

This article focuses on chiral random matrix theories with the global symmetries of quantum chromodynamics (QCD). In particular, it explains how random matrix theory (RMT) can be applied to the spectra of the Dirac operator both at zero chemical potential, when the Dirac operator is Hermitian, and at non-zero chemical potential, when the Dirac operator is non-Hermitian. Before discussing the spectra of these Dirac operators at non-zero chemical potential, the article considers spontaneous symmetry breaking in RMT and the QCD partition function. It then examines the global symmetries of QCD, taking into account the Dirac operator for a finite chiral basis, as well as the global symmetry breaking pattern and the Goldstone manifold in chiral random matrix theory (chRMT). It also describes the generating function for the Dirac spectrum and applications of chRMT to QCD to gauge degrees of freedom.

scholarly journals CHIRAL SYMMETRY BREAKING AT NONZERO CHEMICAL POTENTIAL

2006 ◽  
Vol 21 (04) ◽  
pp. 859-864 ◽  
Author(s):  
J. C. Osborn ◽  
K. Splittorff ◽  
J. J. M. Verbaarschot
Keyword(s):  
Partition Function ◽  
Symmetry Breaking ◽  
Dirac Operator ◽  
Chiral Symmetry ◽  
Chemical Potential ◽  
Chiral Symmetry Breaking ◽  
Chiral Condensate ◽  
Zero Temperature ◽  
Dirac Spectrum

We consider chiral symmetry breaking at nonzero chemical potential and discuss the relation with the spectrum of the Dirac operator. We solve the so called Silver Blaze Problem that the chiral condensate at zero temperature does not depend on the chemical potential while this is not the case for the Dirac spectrum and the weight of the partition function.

scholarly journals Random Matrix Models for the Hermitian Wilson-Dirac operator of QCD-like theories

2012 ◽  
Author(s):  
Savvas Zafeiropoulos ◽  
Mario Kieburg ◽  
Jacobus Verbaarschot
Keyword(s):  
Dirac Operator ◽  
Matrix Models ◽  
Random Matrix ◽  
Random Matrix Models
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