Dynamical Density Fluctuations around QCD Critical Point Based on Dissipative Relativistic Fluid Dynamics-possible fate of Mach cone at the critical point-

Abstract

The purpose of this paper is twofold. Firstly, we study the dynamical density fluctuations around the critical point(CP) of Quantum Chromodynamics(QCD) using dissipative relativistic fluid dynamics in which the coupling of the density fluctuations to those of other conserved quantities is taken into account. We show that the sound mode which is directly coupled to the mechanical density fluctuation is attenuated and in turn the thermal mode becomes the genuine soft mode at the QCD CP. We give a speculation on the possible fate of a Mach cone in the vicinity of the QCD CP as a signal of the existence of the CP on the basis of the above findings. Secondly, we clarify that the so called first-order relativistic fluid dynamic equations have generically no problem to describe fluid dynamic phenomena with long wave lengths contrary to a naive suspect whereas even Israel-Stewart equation, a popular second-order equation, may not describe the hydrodynamic mode in general depending on the value of the relaxation time.

29pages, 4figures; accepted version for publication in Prog. Theor. Phys. Introduction and Sec.3 are somewhat modified to make clearer the purpose of this paper and the discussions on the critical behaviors, respectively. A few references are added. The conclusions are not changed at all

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• Functional renormalization group analysis of the soft mode at the QCD critical point
• Possibility of QCD critical point sweep during black hole formation
• Derivation of relativistic hydrodynamic equations consistent with relativistic Boltzmann equation by renormalization-group method
• Uniqueness of Landau-Lifshitz Energy Frame in Relativistic Dissipative Hydrodynamics
• Relativistic hydrodynamics from projection operator method
• Thermal chiral vortical and magnetic waves: new excitation modes in chiral fluids
• Functional Renormalization Group Study of Phonon Mode Effects on Chiral Critical Point
• Thermal conductivity in dynamics of first-order phase transition
• Roles of axial anomaly on neutral quark matter with color superconducting phase
• Dynamics near QCD critical point by dynamic renormalization group
• Dispersion and suppression of sound near QCD critical point
• Jeans instability analysis in the presence of heat in Eckart's frame
• Nonlinear waves in a hot, viscous and nonextensive quark gluon plasma
• Dynamical spectral structure of density fluctuation near QCD critical point
• Critical Opalescence around the QCD Critical Point and Second-order Relativistic Hydrodynamic Equations Compatible with Boltzmann Equation
• Role of slow, out-of-equilibrium modes on the dynamic structure factor near the QCD critical point
• Dynamics and Stability of Chiral Fluid
• Correlation of density fluctuation in a magnetized QCD matter near the critical end point
• The fate of nonlinear perturbations near the QCD critical point
• Toward Identifying the QCD Critical Point: attenuation of the sound mode around the critical point
• Dynamic density correlations in a baryon rich fluid using Mori-Zwanzig-Nakjima projection operator method
• Microscopic identification of dissipative modes in relativistic field theories