Efimov effect at the Kardar-Parisi-Zhang roughening transition

TL;DR

This paper explores the connection between the KPZ surface growth transition in higher dimensions and the Efimov effect in quantum physics, predicting discrete scale invariance at the transition.

Contribution

It establishes a novel link between the KPZ roughening transition and the Efimov effect, predicting discrete scale invariance in three-dimensional KPZ transitions.

Findings

Predicts Efimov effect at the KPZ transition in 3D.

Suggests the transition exhibits discrete scale invariance.

Links surface growth phenomena with quantum three-body effects.

Abstract

Surface growth governed by the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than two undergoes a roughening transition from smooth to rough phases with increasing the nonlinearity. It is also known that the KPZ equation can be mapped onto quantum mechanics of attractive bosons with a contact interaction, where the roughening transition corresponds to a binding transition of two bosons with increasing the attraction. Such critical bosons in three dimensions actually exhibit the Efimov effect, where a three-boson coupling turns out to be relevant under the renormalization group so as to break the scale invariance down to a discrete one. On the basis of these facts linking the two distinct subjects in physics, we predict that the KPZ roughening transition in three dimensions shows either the discrete scale invariance or no intrinsic scale invariance.