Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2004-02-13
Prog.Theor.Phys.Suppl.153:295-300,2004
Physics
High Energy Physics
High Energy Physics - Lattice
Contribution to the Workshop on ``Finite Density QCD'' (Nara, Japan, 2003-07-10 -- 2003-07-12); 6 pages, 12 figures
Scientific paper
10.1143/PTPS.153.295
We investigate the distribution of the spacings of adjacent eigenvalues of the lattice Dirac operator. At zero chemical potential $\mu$, the nearest-neighbor spacing distribution $P(s)$ follows the Wigner surmise of random matrix theory both in the confinement and in the deconfinement phase. This is indicative of quantum chaos. At nonzero chemical potential, the eigenvalues of the Dirac operator become complex and we discuss how $P(s)$ can be defined in the complex plane. Numerical results from an SU(2) simulation with staggered fermions in fundamental and adjoint representations are compared with predictions from non-hermitian random matrix theory, and agreement with the Ginibre ensemble is found for $\mu\approx 0.5$.
Bittner Elmar
Hands Simon
Markum Harald
Pullirsch Rainer
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