Related papers: QCD, Chiral Random Matrix Theory and Integrability
We propose a new method for simulating QCD at finite density. The method is based on a general factorization property of distribution functions of observables, and it is therefore applicable to any system with a complex action. The…
We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We find a clear separation of the spectrum of eigenvalues into would-be zero modes and…
Two different matrix models for QCD with a non-vanishing quark chemical potential are shown to be equivalent by mapping the corresponding partition functions. The equivalence holds in the phase with broken chiral symmetry. It is exact in…
As we search for an ever deeper understanding of the structure of hadronic matter one of the most fundamental questions is whether or not one can make a connection to the underlying theory of the strong interaction, QCD. We build on recent…
Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model…
We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the…
Scattering of electromagnetic waves in billiard-like systems has become a standard experimental tool of studying properties associated with Quantum Chaos. Random Matrix Theory (RMT) describing statistics of eigenfrequencies and associated…
Since it was first applied to the study of nuclear interactions by Wigner and Dyson, almost 60 years ago, Random Matrix Theory (RMT) has developed into a field of its own within applied mathematics, and is now essential to many parts of…
The zero momentum sectors in effective theories of QCD coupled to pseudoreal (two colors) and real (adjoint) quarks have alternative descriptions in terms of chiral orthogonal and symplectic ensembles of random matrices. Using this…
We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD as well as in quenched U(1) theory on various lattice sizes. As a measure of the fluctuation properties of the eigenvalues, we…
We compute the chiral condensate in 2+1-flavor QCD through the spectrum of low-lying eigenmodes of Dirac operator. The number of eigenvalues of the Dirac operator is evaluated using a stochastic method with an eigenvalue filtering technique…
Several topics in hadron physics at different scales of resolution are discussed. First, deep-inelastic scattering from nucleons and nuclei is viewed in a light-cone coordinate space picture. Then the smooth transition from parton to hadron…
Some exact relations for the spectral density $\rho(\lambda)$ of the Euclidean Dirac operator in $QCD$ are derived. They follow directly from the chiral symmetry of the $QCD$ lagrangian with massless quarks. New results are obtained both in…
Numerical evaluation of the path integral for QCD on a discrete space-time lattice has been used to calculate ground state matrix elements specifying moments of quark density and spin distributions. This talk will explain how these matrix…
We investigate the eigenvalue spectrum of the staggered Dirac matrix in two-color QCD at nonzero temperature and at baryon density when the eigenvalues become complex. The quasi-zero modes and their role for chiral symmetry breaking and the…
The reasons why a considerable effort is made to resolve the low energy structure of QCD are discussed. The effective field theory used for this purpose is illustrated with the recent progress made in the predictions for pipi scattering and…
In this lecture we discuss some exact results for the low-lying spectrum of the Dirac operator in adjoint QCD. In particular, we find an analytical expression for the slope of the average spectral density. These results are obtained by…
Lattice Gauge Theory enables an ab initio study of the low-energy properties of Quantum Chromodynamics, the theory of the strong interaction. I begin these lectures by presenting the lattice formulation of QCD, and then outline the…
Random matrix theory and chiral Lagrangians offer a convenient tool for the exact calculation of microscopic spectral correlators of the Dirac operator in a well-defined finite-volume scaling regime.
We consider random matrix models for the thermodynamic competition between chiral symmetry breaking and diquark condensation in QCD at finite temperature and finite baryon density. The models produce mean field phase diagrams whose topology…