# Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model

## TL;DR

This study numerically investigates the dynamical correlations in a long-range Fermi-Pasta-Ulam model, revealing scale-invariant behavior, mode dispersion consistent with linear theory, and complex lineshapes largely unaffected by interaction decay exponent.

## Contribution

It provides the first detailed numerical analysis of structure factors and dynamical scaling in a long-range FPU model with power-law interactions.

## Key findings

- Propagating modes show dispersion relations matching linear theory.
- Dynamical exponent z varies weakly with interaction decay parameter α.
- Lineshapes of correlations are complex and largely independent of α.

## Abstract

We present a numerical study of dynamical correlations (structure factors) of the long-range generalization of the Fermi-Pasta-Ulam oscillator chain, where the strength of the interaction between two lattice sites decays as a power $\alpha$ of the inverse of their distance. The structure factors at finite energy density display distinct peaks, corresponding to long-wavelength propagating modes, whose dispersion relation is compatible with the predictions of the linear theory. We demonstrate that dynamical scaling holds, with a dynamical exponent $z$ that depends weakly on $\alpha$ in the range $1<\alpha<3$. The lineshapes have a non-trivial functional form and appear somehow independent of $\alpha$. Within the accessible time and size ranges, we also find that the short-range limit is hardly attained even for relatively large values of $\alpha$.