  It is shown, that parity violation in quantum systems can be a natural result
of their dynamical evolution. The corresponding (completely integrable)
formalism is based on the use of quantum theory with complex time and
non-Hermitian Hamiltonian. It is demonstrated, that starting with total
symmetry between left and right states at the initial time, one obtains
strictly polarized system at the time infinity. The increasing left-right
asymmetry detects a presence of well-defined arrow of time in evolution of the
system. We discuss possible application of the general formalism developed to
construction of modified irreversible dynamics of massless Dirac fields (in
framework of superstring theory, for example).
