The effect of time-dependent coupling on non-equilibrium steady states

TL;DR

This paper investigates how time-dependent coupling affects non-equilibrium steady states in a quantum system, deriving formulas for stationary charge current and showing invariance to switching details.

Contribution

It introduces a method to compute NESS in quantum systems with time-dependent coupling and demonstrates invariance properties of the steady state and current.

Findings

Non-equilibrium steady states are independent of switching details.

Derived Landau-Lifschitz and Landauer-Buttiker formulas for current.

Stationary charge current shows invariance under coupling variations.

Abstract

Consider (for simplicity) two one-dimensional semi-infinite leads coupled to a quantum well via time dependent point interactions. In the remote past the system is decoupled, and each of its components is at thermal equilibrium. In the remote future the system is fully coupled. We define and compute the non equilibrium steady state (NESS) generated by this evolution. We show that when restricted to the subspace of absolute continuity of the fully coupled system, the state does not depend at all on the switching. Moreover, we show that the stationary charge current has the same invariant property, and derive the Landau-Lifschitz and Landauer-Buttiker formulas.