We check SU(2)-Yang-Mills theory with fermions in adjoint representation against quantum chaos when a chemical potential is switched on. Then the eigenvalues be come complex and one has to compare with the Bohigas-Giannoni-Schmit conjecture for the Ginibre distribution. Actually, we find a transition from Wigner to Gini bre behavior across the density phase transition. Quantum chaos persists deep in to the high-density phase in agreement with random matrix theory. Generally, we discuss random matrix theory as a tool to discriminate between a valid model Ham iltonian and an analytically solvable Hamiltonian or experimental data.