Adiabatic non-equilibrium steady states in the partition free approach

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