[Paper Review] Critical acoustics and singular bulk viscosity of quark matter

B. O. Kerbikov|arXiv (Cornell University)|Jun 26, 2018

High-Energy Particle Collisions Research1 references3 citations

TL;DR

This paper develops a dynamical model for quark matter near a second-order QCD phase transition, showing that critical fluctuations of the order parameter lead to a singular bulk viscosity and enhanced sound attenuation. Using a fluctuation propagator and Aslamazov-Larkin diagrams, it derives a t^{-3/2} divergence in bulk viscosity and sound absorption near T_c, closely matching universal scaling laws.

ABSTRACT

We examine the behavior of sound attenuation and bulk viscosity near the 2'nd order QCD phase transition at finite density. A dynamical model is presented describing the coupled evolution of sound mode and a slow mode of fluctuations.

Motivation & Objective

• To understand the anomalous behavior of sound attenuation and bulk viscosity near the QCD chiral phase transition at finite baryon density.
• To resolve the discrepancy between hydrodynamic models and universal scaling laws in critical phenomena for quark matter.
• To model the coupling between hydrodynamic sound modes and slow order-parameter fluctuations near T_c.
• To derive the temperature dependence of bulk viscosity and sound absorption using a dynamical model based on fluctuation propagators.
• To connect the singular behavior of transport coefficients to the critical dynamics of quark pairing in 2SC superconducting quark matter.

Proposed method

• Uses a dynamical model coupling sound modes with a slow order-parameter mode via the Mandelshtam-Leontovich mechanism.
• Derives the fluctuation propagator (FP) for quark pair fluctuations in the 2SC phase using Dyson or time-dependent Landau-Ginzburg equations with Langevin noise.
• Applies the Kubo formalism to express bulk viscosity and sound absorption in terms of pressure-pressure correlation functions.
• Identifies the Aslamazov-Larkin (AL) diagram as the dominant contribution to the correlation function near T_c.
• Evaluates the imaginary part of the AL polarization operator, finding a t^{-3/2} dependence in the critical regime.
• Relates the dimensionless sound absorption per wavelength α_λ to the bulk viscosity via α_λ ∝ ωζ(0)/εc₀², leading to α_λ ∝ t^{-3/2} ln²(Λ/2πT_c).

Experimental results

Research questions

• RQ1 How does the bulk viscosity of quark matter diverge near the second-order chiral phase transition?
• RQ2 What is the origin of the anomalous sound attenuation in quark matter close to T_c?
• RQ3 How do critical fluctuations of the order parameter modify the hydrodynamic behavior of quark matter?
• RQ4 To what extent does the t^{-3/2} scaling of bulk viscosity match the universal scaling prediction ζ ∝ t^{-zν + α}?
• RQ5 What role does the Aslamazov-Larkin diagram play in determining the critical behavior of transport coefficients?

Key findings

• The bulk viscosity ζ exhibits a t^{-3/2} temperature dependence near T_c, closely matching the universal scaling law ζ ∝ t^{-zν + α} with z ≈ 3, ν ≈ 0.6, and α ≈ 0.11.
• The sound absorption coefficient per wavelength, α_λ, scales as t^{-3/2} ln²(Λ/2πT_c), indicating strong anomalous attenuation near the critical point.
• The imaginary part of the Aslamazov-Larkin polarization operator scales as t^{-3/2}, which dominates the pressure-pressure correlation function near T_c.
• The model predicts a singular increase in bulk viscosity due to coupling between sound modes and slow order-parameter fluctuations, consistent with the Mandelshtam-Leontovich mechanism.
• The electrical conductivity from the same diagram shows a t^{-1/2} dependence, indicating distinct critical scaling for different transport coefficients.
• The derived t^{-3/2} scaling for α_λ and ζ is in good quantitative agreement with the expected critical behavior, validating the model's physical consistency.