# Non-linear Fluctuating Hydrodynamics with many conserved fields: the case of a 3D anharmonic chain

## TL;DR

This paper extends non-linear fluctuating hydrodynamics to a 3D anharmonic chain with multiple conserved fields, analyzing mode behaviors and comparing theoretical predictions with molecular dynamics simulations at high temperatures.

## Contribution

It develops a 3D model within NLFHT, identifying distinct diffusive and superdiffusive behaviors of modes, and provides detailed correlation analyses.

## Key findings

- Transverse modes are diffusive.
- Heat and longitudinal modes are superdiffusive.
- Good agreement between theory and simulations at high temperatures.

## Abstract

We propose a model for a chain vibrating in 3 dimensions (3D), with first neighbors anharmonic interatomic potential which depends on their distance, and subjected to an external tension. In the framework of the non-linear fluctuating hydrodynamic theory (NLFHT), that was successfully applied to 1D chains, we obtain a heat mode, two longitudinal and four transverse sound modes. We compute their spatio-temporal correlations comparing the theoretical results with molecular dynamics simulations, finding a good agreement for high temperatures. We find that the transverse sound modes behave diffusively, meanwhile the heat and longitudinal sound modes superdiffusively, exploring their possible scaling functions and characteristic exponents.