Integrability and coherence of hopping between 1D correlated electron systems (Reply Comment)

TL;DR

This paper discusses the distinction between integrability effects and coherence in electron hopping between 1D correlated systems, emphasizing different temporal regimes and clarifying prior interpretations.

Contribution

It clarifies that integrability influences intermediate-time behavior, while coherence pertains to long-time dynamics, addressing misconceptions in previous analyses.

Findings

Integrability affects intermediate-time electron dynamics.

Coherence relates to long-time electron behavior.

Numerical investigations of spectral function and conductivity support these distinctions.

Abstract

The main point of Clarke and Strong's comment, namely that our results concerning the effect of integrability on the hopping of electrons between chains are probably not related to the notion of coherence proposed in \cite{clarke}, is important and well taken. In fact, we have already stressed in our work that integrability affects the intermediate-time behaviour but not the short-time one, while in \cite{clarke} the authors make predictions about the long-time dynamics on the basis of a calculation at short times. The logical conclusion is then that these two effects are in fact different phenomena. In more recent papers we have numerically investigated other physical quantities (spectral function, transverse conductivity in relation to the notion of coherence developed in \cite{clarke}.