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arXiv · 1903.07176

Janossy densities for chiral random matrix ensembles and their applications to two-color QCD

Hiroyuki Fuji·Issaku Kanamori·Shinsuke M. Nishigaki
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Abstract

We compute individual distributions of low-lying eigenvalues of massive chiral random matrix ensembles by the Nystr\"om-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 Nystr\"om-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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BibTeXRIS

Hiroyuki Fuji, Issaku Kanamori, Shinsuke M. Nishigaki. 2019-03-17. Janossy densities for chiral random matrix ensembles and their applications to two-color QCD. https://doi.org/10.1007/jhep08(2019)053

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