Lagrangian formulation and symmetrical description of liquid dynamics

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.

arXiv commentPhysical Review E 96, 062134 (2017)

References in corpus (5)

• Collective modes and thermodynamics of the liquid state
• Nonrelativistic effective Lagrangians
• Emergence and evolution of $k$-gap in spectra of liquid and supercritical states
• Understanding the problem of glass transition on the basis of elastic waves in a liquid
• Stable equilibrium point and oscillatory motion of the Universe in a model with variable vacuum energy

Cited by in corpus (15)

• Universal origin of boson peak vibrational anomalies in ordered crystals and in amorphous materials
• Gapped momentum states
• Onset of transverse (shear) waves in strongly-coupled Yukawa fluids
• Collective modes and gapped momentum states in liquid Ga: experiment, theory and simulation
• Low frequency propagating shear waves in holographic liquids
• Maxwell interpolation and close similarities between liquids and holographic models
• Elasticity bounds from Effective Field Theory
• Field Theory of Dissipative Systems with Gapped Momentum States
• Quantum dissipation in a scalar field theory with gapped momentum states
• Unexpected thermo-elastic effects in liquid glycerol by mechanical deformation
• Molecular hydrodynamic theory of the velocity autocorrelation function
• Strain-Induced Violation of Temperature Uniformity in Mesoscale Liquids
• Dissipation and energy gap
• Generally applicable physics-based equation of state for liquids
• Identification of Mechano-stimuli (Linear to Harmonic) Thermal Response in Mesoscopic Liquids