Adiabatic non-equilibrium steady states in the partition free approach

Consider a small sample coupled to a finite number of leads and
assume that the total (continuous) system is at thermal equilibrium in
the remote past. We construct a non-equilibrium steady state (NESS) by
adiabatically turning on an electrical bias between the leads. The main
mathematical challenge is to show that certain adiabatic wave operators
exist and to identify their strong limit when the adiabatic parameter tends
to zero. Our NESS is different from, though closely related with the NESS
provided by the Jakic–Pillet–Ruelle approach. Thus we partly settle a
question asked by Caroli et al. (J. Phys. C Solid State Phys. 4(8):916–
929, 1971) regarding the (non)equivalence between the partitioned and
partition-free approaches.