Efimov effect at the Kardar-Parisi-Zhang roughening transition

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.

7 pages, 4 figures; published version

References in corpus (6)

• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Nonrelativistic conformal field theories
• The one-dimensional KPZ equation and its universality class
• Universal Relations for Identical Bosons from 3-Body Physics
• Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension
• Multi-surface coding simulations of the restricted solid-on-solid model in four dimensions

Cited by in corpus (4)

• Second root of dilute Bose-Fermi mixtures
• Universal bound states and resonances with Coulomb plus short-range potentials
• Efimovian states of three charged particles
• Bound-like State in a 1D Self-Similar Delta-Barrier Array