Adiabatic non-equilibrium steady states in the partition free approach

TL;DR

This paper constructs a non-equilibrium steady state in a quantum system with leads by adiabatically applying a bias, addressing mathematical challenges in wave operator limits and clarifying differences between two theoretical approaches.

Contribution

It develops a rigorous method to construct NESS in the partition-free approach and clarifies its relation to the partitioned approach, settling a longstanding question.

Findings

Existence of adiabatic wave operators established.

Constructed NESS differs from the Jakšić-Pillet-Ruelle approach.

Clarified the relationship between partitioned and partition-free approaches.

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{\'c}-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.