Phonon-mediated Casimir interaction between mobile impurities in one-dimensional quantum liquids

TL;DR

This paper investigates how virtual phonons in one-dimensional quantum liquids mediate a long-range Casimir-like interaction between mobile impurities, with the interaction's sign and magnitude depending on impurity-phonon scattering properties.

Contribution

It reveals a universal $1/r^3$ decay of the phonon-mediated interaction and discusses how tuning impurity parameters can switch the interaction from attractive to repulsive.

Findings

Interaction decays as $1/r^3$, slower than van der Waals.

Sign of interaction depends on impurity-phonon scattering amplitudes.

Tuning impurities near integrable points can reverse interaction sign.

Abstract

Virtual phonons of a quantum liquid scatter off impurities and mediate a long-range interaction, analogous to the Casimir effect. In one dimension the effect is universal and the induced interaction decays as $1/r^3$, much slower than the van der Waals interaction $\sim1/r^6$, where $r$ is the impurity separation. The sign of the effect is characterized by the product of impurity-phonon scattering amplitudes, which take a universal form and have been seen to vanish for several integrable impurity models. Thus, if the impurity parameters can be independently tuned to lie on opposite sides of such integrable points, one can observe an attractive interaction turned into a repulsive one.