相关论文: Chiral Random Matrix Model at Finite Chemical Pote…

In the $\varepsilon$-regime of chiral perturbation theory the spectral correlations of the Euclidean QCD Dirac operator close to the origin can be computed using random matrix theory. To incorporate the effect of temperature, a random…

We will report recent progress on the QCD phase diagram at finite temperature and density. In particular, we discuss the universal scaling of the chiral transition in the limit of two massless quarks and one strange quark. We also discuss…

We study the eigenvalue behaviour of large complex correlated Wishart matrices near an interior point of the limiting spectrum where the density vanishes (cusp point), and refine the existing results at the hard edge as well. More…

Macroscopic properties of the strong interaction near its chiral phase transition exhibit scaling behaviors, which are the same as those observed close to the magnetic transition in a 3-dimensional classical spin system with $O(4)$…

We reveal that the universal scaling properties of the chiral phase transition in quantum chromodynamics (QCD) at the macroscale are, in fact, encoded within the microscopic energy levels of its fundamental constituents, the quarks. We…

We show that the derivative of the logarithm of the average characteristic polynomial of a diffusing Wishart matrix obeys an exact partial differential equation valid for an arbitrary value of N, the size of the matrix. In the large N…

We review the application of random matrix theory (RMT) to chiral symmetry in QCD. Starting from the general philosophy of RMT we introduce a chiral random matrix model with the global symmetries of QCD. Exact results are obtained for…

We present a hydrodynamical description of the QCD Dirac spectrum at finite chemical potential as an uncompressible droplet in the complex eigenvalue space. For a large droplet, the fluctuation spectrum around the hydrostatic solution is…

We show that for small values of the chemical potential the curvature of the phase transition line can be deduced from an analysis of scaling properties of the chiral condensate and its susceptibilities. We make use of a recent analysis of…

In this talk we review some recent results from random matrix models as applied to some non-perturbative issues in QCD. All of the issues we will discuss touched upon the important phenomenon related to the spontaneous breaking of chiral…

We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential mu. In this…

Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^\dagger M where M is a complex matrix drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A and B…

We use a random matrix model to study chiral symmetry breaking in QCD at finite chemical potential $\mu$. We solve the model and compute the eigenvalue density of the Dirac matrix on a complex plane. A naive ``replica trick'' fails for…

In this lecture we discuss various aspects of QCD at nonzero chemical potential, including its phase diagram and the Dirac spectrum, and summarize what chiral random matrix theory has contributed to this subject. To illustrate the…

We introduce a one-parameter deformation of the Wishart-Laguerre or chiral ensembles of positive definite random matrices with Dyson index beta=1,2 and 4. Our generalised model has a fat-tailed distribution while preserving the invariance…

We introduce three universality classes of chiral random matrix ensembles with a nonzero chemical potential and real, complex or quaternion real matrix elements. In the thermodynamic limit we find that the distribution of the eigenvalues in…

Phase diagram of a chiral random matrix model with the degenerate ud quarks and the s quark at finite temperature and density is presented. The model exhibits a first-order transition at finite temperature for three massless flavors, owing…

We study scaling behavior of a chiral order parameter performing a simulation of two-flavor QCD with improved Wilson quarks. It has been shown that the scaling behavior of the chiral order parameter defined by a Ward-Takahashi identity…

According to the Banks-Casher formula the chiral order parameter is directly related to the spectrum of the Dirac operator. In this lecture, we will argue that some properties of the Dirac spectrum are universal and can be obtained from a…

We study the scaling behavior of the (2+1)-flavor QCD crossover region towards the chiral limit with smaller-than-physical light quark mass gauge ensembles, generated using the HISQ fermion discretization. At zero chemical potential, we…