Adiabatic non-equilibrium steady states in the partition free approach

Abstract

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 Jak{\v s}i{ć}-Pillet-Ruelle approach. Thus we partly settle a question asked by Caroli {\it et al} in 1971 regarding the (non)equivalence between the partitioned and partition-free approaches.

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Cited by in corpus (9)

• On the steady state correlation functions of open interacting systems
• Cumulant generating function formula of heat transfer in ballistic system with lead-lead coupling
• Landauer transport as a quasisteady state on finite chains under unitary quantum dynamics
• Memory effects in non-interacting mesoscopic transport
• Adiabatic theorems for general linear operators with time-independent domains
• On the self-consistent Landauer-Büttiker formalism
• Mean--field stability for the junction of quasi 1D systems with Coulomb interactions
• A Dyson equation for non-equilibrium Green's functions in the partition-free setting
• A Geometric Approach to the Landauer-Büttiker Formula