Nonlinear fluctuating hydrodynamics with many conserved fields: The case of a three-dimensional anharmonic chain

We propose a model for a chain vibrating in three dimensions, with first neighbors anharmonic interatomic potential, which depends on their distance, and subjected to an external tension. In the framework of the nonlinear fluctuating hydrodynamic theory, which was successfully applied to one-dimensional chains, we obtain a heat mode, two longitudinal, and four transverse sound modes. We compute their spatiotemporal 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 behave superdiffusively, exploring their possible scaling functions and characteristic exponents.