  We present a method to perform stability analysis of nonequilibrium fixed
points appearing in self-consistent electron transport calculations. The
nonequilibrium fixed points are given by the self-consistent solution of
stationary, nonlinear kinetic equation for single-particle density matrix. We
obtain the stability matrix by linearizing the kinetic equation around the
fixed points and analyze the real part of its spectrum to assess the asymptotic
time behavior of the fixed points. We derive expressions for the stability
matrices within Hartree-Fock and linear response adiabatic time-dependent
density functional theory. The stability analysis of multiple fixed points is
performed within the nonequilibrium Hartree-Fock approximation for the electron
transport through a molecule with a spin-degenerate single level with local
Coulomb interaction.
