Dynamical structure factor of a nonlinear Klein-Gordon lattice

TL;DR

This paper numerically computes the dynamical structure factor of a nonlinear Klein-Gordon lattice to analyze phonon bound states and inelastic scattering, demonstrating the method's effectiveness beyond weak anharmonicity.

Contribution

It introduces a numerical approach to study the dynamical structure factor of nonlinear Klein-Gordon lattices, capturing spectra of nonlinear phonons beyond weak anharmonicity.

Findings

Identification of phonon bound states due to on-site nonlinearity

Dependence of inelastic scattering on anharmonicity

Method applicable to strong anharmonic regimes

Abstract

The quantum modes of a nonlinear Klein-Gordon lattice have been computed numerically [L. Proville, Phys. Rev. B 71, 104306 (2005)]. The on-site nonlinearity has been found to lead to phonon bound states. In the present paper, we compute numerically the dynamical structure factor so as to simulate the coherent scattering cross section at low temperature. The inelastic contribution is studied as a function of the on-site anharmonicity. Interestingly, our numerical method is not limited to the weak anharmonicity and permits one to study thoroughly the spectra of nonlinear phonons.