Quantum chaos and QCD at finite chemical potential

We investigate the distribution of the spacings of adjacent eigenvalues of the lattice Dirac operator. At zero chemical potential mu, the nearest-neig hbor spacing distribution P(s) follows the Wigner surmise of random matrix theory both in the confinement and in the deconfinement phase. This is indi cative of quantum chaos. At nonzero chemical potential, the eigenvalues of the Dirac operator become complex. We discuss how P(s) can be defined in th e complex plane. Numerical results from an SU(3) simulation with staggered fermions are compared with predictions from non-hermitian random matrix the ory, and agreement with the Ginibre ensemble is found for mu approximate to 0.7.