Non-equilibrium Green's function formalism and the problem of bound   states
  The non-equilibrium Green's function formalism for infinitely extended reservoirs coupled to a finite system can be derived by solving the equations of motion for a tight-binding Hamiltonian. While this approach gives the correct density for the continuum states, we find that it does not lead, in the absence of any additional mechanisms for equilibration, to a unique expression for the density matrix of any bound states which may be present. Introducing some auxiliary reservoirs which are very weakly coupled to the system leads to a density matrix which is unique in the equilibrium situation, but which depends on the details of the auxiliary reservoirs in the non-equilibrium case. 
Abhishek Dhar (1) and Diptiman Sen (2) ((1) RRI, Bangalore, (2) IISc,   Bangalore)