Related papers: Handbook Article on Applications of Random Matrix …
Using an integration formula recently derived by Conrey, Farmer and Zirnbauer, we calculate the expectation value of the phase factor of the fermion determinant for the staggered lattice QCD action in one dimension. We show that the…
We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral Perturbation Theory and chiral Random Matrix Theory. A graded chiral Lagrangian is used to evaluate the microscopic…
We analyze the smallest Dirac eigenvalues by formulating an effective theory for the QCD Dirac spectrum. We find that in a domain where the kinetic term of the effective theory can be ignored, the Dirac eigenvalues are distributed according…
In a deep-infrared (ergodic) regime, QCD coupled to massive pseudoreal and real quarks are described by chiral orthogonal and symplectic ensembles of random matrices. Using this correspondence, general expressions for the QCD partition…
For QCD at non-zero chemical potential $\mu$, the Dirac eigenvalues are scattered in the complex plane. We define a notion of ordering for individual eigenvalues in this case and derive the distributions of individual eigenvalues from…
We derive the hole probability and the distribution of the smallest eigenvalue of chiral hermitian random matrices corresponding to Dirac operators coupled to massive quarks in QCD. They are expressed in terms of the QCD partition function…
We study the spectrum of the QCD Dirac operator near zero virtuality for $N_c =2$. According to a universality argument, it can be described by a random matrix theory with the chiral structure of QCD, but with $real$ matrix elements. Using…
We present two pieces of evidence in support of the conjecture that the microscopic spectral density of the Dirac operator is a universal quantity. First, we compare lattice data to predictions from random matrix theory. Second, we show…
We analyze the statistical properties of the spectrum of the QCD Dirac operator at low energy in a finite box of volume $L^4$ by means of partially quenched Chiral Perturbation Theory (pqChPT), a low-energy effective field theory based on…
Resent developments in the Random Matrix and Random Lattice Theories give a possibility to find low-energy theorems for many physical models in the Born-Infeld form. In our approach that based on the Random Lattice regularization of QCD we…
We analyze how individual eigenvalues of the QCD Dirac operator at nonzero quark chemical potential are distributed in the complex plane. Exact and approximate analytical results for both quenched and unquenched distributions are derived…
We study the eigenvalue spectrum of different lattice Dirac operators (staggered, fixed point, overlap) and discuss their dependence on the topological sectors. Although the model is 2D (the Schwinger model with massless fermions) our…
We investigate the eigenvalue spectrum of the staggered Dirac matrix in full QCD with two colors and finite chemical potential. Along the strong-coupling axis up to the temperature phase transition, the low-lying Dirac spectrum is well…
We show that, with an appropriate choice of a Dirac operator, there is a remnant of chiral anomalies in the reduced model in which there is no coordinate dependences of the gauge field. This result is obtained by exploring a topological…
The microscopic spectral density of the QCD Dirac operator at nonzero baryon chemical potential for an arbitrary number of quark flavors was derived recently from a random matrix model with the global symmetries of QCD. In this paper we…
We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of…
We consider non-Hermitian Dirac operators in QCD-like theories coupled to a chiral U(1) potential or an imaginary chiral chemical potential. We show that in the continuum they fall into the recently discovered universality classes…
It was established that distribution of the near-zero modes of the Dirac operator is consistent with the Chiral Random Matrix Theory (CRMT) and can be considered as a consequence of spontaneous breaking of chiral symmetry (SBCS) in QCD. The…
We introduce a new non-Hermitian random matrix model for QCD with a baryon chemical potential. This model is a direct chiral extension of a previously studied model that interpolates between the Wigner-Dyson and Ginibre ensembles. We…
We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For $N_f$ flavors, the chiral flavor symmetry of these theories is…