Symmetry-based nonlinear fluctuating hydrodynamics in one dimension

TL;DR

This paper develops a symmetry-based nonlinear fluctuating hydrodynamics framework for 1D many-particle systems, identifying KPZ universality and confirming it through numerical simulations.

Contribution

It introduces a novel, symmetry-driven derivation of NFH equations for 1D systems, linking them to KPZ universality class.

Findings

Confirmed KPZ dynamical exponent z=3/2 for sound and heat modes.

Numerical simulations match KPZ and Prahofer-Spohn universal scaling functions.

Established a unified symmetry-based approach for 1D nonequilibrium transport.

Abstract

We present a symmetry-based formulation of nonlinear fluctuating hydrodynamics (NFH) for one-dimensional many-particle systems with generic homogeneous nearest-neighbor interactions. We derive the hydrodynamic equations solely from symmetry and conservation principles, ensuring full consistency with thermalization. Using the dynamic renormalization group, we identify a KPZ-type fixed point, characterized by the dynamical exponent $z=3/2$ for both the sound and heat modes. Extensive numerical simulations of the derived NFH equations confirm this exponent and further reveal that both modes are close to the universal KPZ scaling function, the Prahofer-Spohn function. These findings establish a unified, symmetry-based framework for understanding universal transport and fluctuation phenomena in one-dimensional nonequili brium systems, independent of microscopic details.