Lagrangian formulation and symmetrical description of liquid dynamics

TL;DR

This paper introduces a symmetrical Lagrangian framework for liquid dynamics, unifying hydrodynamic and solid-like descriptions, and predicts the existence of two propagating gapped waves with implications for understanding liquid properties.

Contribution

It develops a novel two-field Lagrangian formulation that treats dissipative hydrodynamic and solid-like terms equally, revealing new insights into liquid wave propagation.

Findings

Prediction of two gapped waves propagating in opposite directions

Demonstration of symmetry between hydrodynamic and solid-like descriptions

Identification of conditions where gaps close and dissipative effects dominate

Abstract

Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in $k$-space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field Lagrangian of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The Lagrangian predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in $k$-space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.