Oscillating Casimir force between impurities in one-dimensional Fermi liquids

TL;DR

This paper investigates how two impurities in a one-dimensional Fermi liquid interact via an oscillating Casimir force, which depends on their separation and exhibits Friedel oscillation patterns.

Contribution

The study extends previous work by showing the oscillatory nature and sign dependence of the Casimir interaction on impurity separation in 1D Fermi liquids.

Findings

Casimir interaction oscillates with impurity separation

Maxima of interaction align with tunneling resonances

Interaction sign and strength are highly sensitive to separation

Abstract

We study the interaction of two localized impurities in a repulsive one-dimensional Fermi liquid via bosonization. In a previous paper [Phys. Rev. A 72, 023616 (2005)], it was shown that at distances much larger than the interparticle spacing the impurities interact through a Casimir-type force mediated by the zero sound phonons of the underlying quantum liquid. Here we extend these results and show that the strength and sign of this Casimir interaction depend sensitively on the impurities separation. These oscillations in the Casimir interaction have the same period as Friedel oscillations. Their maxima correspond to tunneling resonances tuned by the impurities separation.