  A nonperturbative lattice study of QCD at finite chemical potential is
complicated due to the complex fermion determinant and the sign problem. Here
we apply the method of stochastic quantization and complex Langevin dynamics to
this problem. We present results for U(1) and SU(3) one link models and QCD at
finite chemical potential using the hopping expansion. The phase of the
determinant is studied in detail. Even in the region where the sign problem is
severe, we find excellent agreement between the Langevin results and exact
expressions, if available. We give a partial understanding of this in terms of
classical flow diagrams and eigenvalues of the Fokker-Planck equation.
