Comment on ``Integrability and Coherence of Hopping between 1D Correlated Electron Systems''

TL;DR

This paper critiques recent numerical studies on coupled 1D electron liquids, emphasizing that observed integrability effects relate more to ergodicity than coherence, and suggests a better measure for coherence in interliquid hopping.

Contribution

It clarifies the role of integrability in coupled 1D electron systems and proposes a more suitable metric for assessing coherence in interliquid hopping.

Findings

Integrability impacts ergodicity, not coherence.

The quantity < δN(t) > better indicates coherence.

Critique of previous numerical interpretations.

Abstract

We comment on recent numerical studies concerning coupled 1D electron liquids (F. Mila and D. Poilblanc, Phys. Rev. Lett. 76, 287 (1996)). In particular, we point out that the importance of integrability observed in the results of these authors for the quantity $P(t)$ is really an indication of the importance of integrability for questions of ergodicity, rather than questions of coherence. We discuss why this is so, and why the quantity $< \delta N (t) >$ is a more appropriate function for determining whether or not interliquid hopping is coherent.