  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 $\mu\approx 0.5$.
