On adiabatic turn-on and the asymptotic limit in linear response theory for open systems

TL;DR

This paper clarifies the correct limiting procedure in linear response theory for open systems, demonstrating that surface terms vanish when the system size limit precedes the adiabatic limit, ensuring gauge invariance without modifying the continuity equation.

Contribution

It establishes the importance of limit order in linear response derivations for open systems, resolving recent claims about gauge invariance and simplifying the derivation of Landauer-Büttiker equations.

Findings

Surface terms vanish with correct limit order

Linear response theory is gauge-invariant without modifications

Simplified derivation of Landauer-Büttiker equations

Abstract

Linear response theory for open (infinite) systems leads to an expression for the current response which contains surface terms in addition to the usual bulk Kubo term. We show that this surface term vanishes identically if the correct order of limits is maintained in the derivation: the system size, L, must be taken to infinity before the adiabatic turn-on rate $\delta$ of the perturbation is taken to zero. In contrast to recent claims this shows that linear response theory for open systems is gauge-invariant without modification of the continuity equation. We show that a simpler derivation of the Landauer-B\"uttiker equations may be obtained consistently from the bulk Kubo term, noting that surface terms arising here are non-vanishing because they involve the opposite order of limits, $\delta \to 0$, then $L \to \infty$.