Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1998-09-10
Nucl.Phys.Proc.Suppl. 73 (1999) 486-488
Physics
High Energy Physics
High Energy Physics - Lattice
LATTICE98(hightemp), 3 pages, 10 figures
Scientific paper
10.1016/S0920-5632(99)85113-5
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. We discuss how $P(s)$ can be defined in the complex plane. Numerical results from an SU(3) simulation with staggered fermions are compared with predictions from non-hermitian random matrix theory, and agreement with the Ginibre ensemble is found for $\mu\approx 0.7$.
Markum Harald
Pullirsch Rainer
Rabitsch K.
Wettig Tilo
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