  Quantum disordered problems with a direction (imaginary vector-potential) are
discussed and mapped onto a supermatrix sigma-model. It is argued that the $0D$
version of the sigma-model may describe a broad class of phenomena that can be
called directed quantum chaos. It is demonstrated by explicit calculations that
these problems are equivalent to problems of theory of random asymmetric or
non-Hermitian matrices. A joint probability of complex eigenvalues is obtained.
The fraction of states with real eigenvalues proves to be always finite for
time reversal invariant systems.
