- August 2019 – April2020, M.Sc. Thesis project
- Guide: Dr. Subhasis Basak, School of Physical Sciences, NISER
Abstract: With an introduction to the random matrix theory (RMT), the application of random matrices to describe the spectrum of Wilson fermions and staggered fermions is demonstrated. It is shown that the eigenvalues of random matrices from gaussian ensembles are confined in a single interval of the real line and the eigenvalues repel each other. For large-N dimensional Gaussian random matrices, it is shown by using the Coulomb gas technique, that the eigenvalues tend to be distributed by a semicircular distribution function. From the joint probability density of the eigenvalues, the normal modes of fluctuation of the eigenvalues about their mean position were calculated. In the application part, the spectrum of Wilson fermion was obtained for a two-color case, by replacing the gauge fields by random matrices from the Gaussian orthogonal ensemble (GOE). The unfolding procedure was demonstrated for the case of GOE eigenvalues. For the staggered fermion case, which respects chiral symmetry, the chiral random matrix ensemble was used. In this case, the eigenvalues obtained from RMT and those obtained from lattice quantum chromodynamics (lattice QCD) were first unfolded, and then they were compared to show that they match atleast in some regime.