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Register a new userJanossy densities for chiral random matrix ensembles and their applications to two-color QCD
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We compute individual distributions of low-lying eigenvalues of massive chiral random matrix ensembles by the Nystrom-type quadrature method for evaluating the Fredholm determinant and Pfaffian that represent the analytic continuation of the Janossy densities (conditional gap probabilities). A compact formula for individual eigenvalue distributions suited for precise numerical evaluation by the Nystrom-type method is obtained in an explicit form, and the $k^{rm{small th}}$ smallest eigenvalue distributions are numerically evaluated for chiral unitary and symplectic ensembles in the microscopic limit. As an application of our result, the low-lying Dirac spectra of the SU(2) lattice gauge theory with $N_F=8$ staggered flavors are fitted to the numerical prediction from the chiral symplectic ensemble, leading to a precise determination of the chiral condensateof a two-color QCD-like system in the future.
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Two-color finite density QCD is free from the sign problem, and it is thus regarded as a good model to check the validity of the analytic continuation method. We study the method in terms of the corresponding chiral random matrix model. It is found that at temperatures slightly higher than the pseudo critical temperature, the ratio type of extrapolated function works well in accordance with the results of the Monte Carlo simulations.
The phase diagram of two-color QCD with a chiral chemical potential is studied on the lattice. The focus is on the confinement/deconfinement phase transition and the breaking/restoration of chiral symmetry. The simulations are carried out with dynamical staggered fermions without rooting. The dependence of the Polyakov loop, the chiral condensate and the corresponding susceptibilities on the chiral chemical potential and the temperature are presented.
Using operator methods, we generally present the level densities for kinds of random matrix unitary ensembles in weak sense. As a corollary, the limit spectral distributions of random matrices from Gaussian, Laguerre and Jacobi unitary ensembles are recovered. At the same time, we study the perturbation invariability of the level densities of random matrix unitary ensembles. After the weight function associated with the 1-level correlation function is appended a polynomial multiplicative factor, the level density is invariant in the weak sense.
Theory of Random Matrix Ensembles have proven to be a useful tool in the study of the statistical distribution of energy or transmission levels of a wide variety of physical systems. We give an overview of certain q-generalizations of the Random Matrix Ensembles, which were first introduced in connection with the statistical description of disordered quantum conductors.
We study the cold and dense regime in the phase diagram of two-color QCD with heavy quarks within a three-dimensional effective theory for Polyakov loops. This theory is derived from two-color QCD in a combined strong-coupling and hopping expansion. In particular, we study the onset of diquark density as the finite-density transition of the bosonic baryons in the two-color world. In contrast to previous studies of heavy dense QCD, our zero-temperature extrapolations are consistent with a continuous transition without binding energy. They thus provide evidence that the effective theory for heavy quarks is capable of describing the characteristic differences between diquark condensation in two-color QCD and the liquid-gas transition of nuclear matter in QCD.
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