Effective phonon treatment of asymmetric interparticle interaction potentials

TL;DR

This paper introduces an effective phonon approach for one-dimensional lattices with asymmetric interparticle potentials, approximating the potential as piecewise harmonic to accurately describe phonon behavior.

Contribution

The authors develop a novel method to treat asymmetric interparticle interactions by dividing and approximating potentials with effective harmonic force constants.

Findings

Effective phonon frequencies match numerical results

Method accurately describes asymmetric potential systems

Approach simplifies analysis of complex interparticle interactions

Abstract

We propose an effective phonon treatment in one dimensional momentum-conserved lattice system with asymmetric interparticle interaction potentials. Our strategy is to divide the potential into two segments by the zero-potential point, and then approximate them by piecewise harmonic potentials with effective force constants $\tilde{k}_L$ and $\tilde{k}_R$ respectively. The effective phonons can then be well described by $\omega_c=\sqrt{2(\tilde{k}_L+\tilde{k}_R)}% |sin(\frac{1}{2}aq)|$. The numerical verifications show that this treatment works very well.