Characteristic momentum of Hydro+ and a bound on the speed of sound near the QCD critical point

Abstract

Near the critical point in the QCD phase diagram, hydrodynamics breaks down at a momentum where the frequency of the fastest hydrodynamic mode becomes comparable with the decay rate of the slowest non-hydrodynamic mode. Hydro+ was developed as a framework which extends the range of validity of hydrodynamics beyond that momentum value. This was achieved through coupling the hydrodynamic modes to the slowest non-hydrodynamic mode. In this work, analyzing the spectrum of linear perturbations in Hydro+, we find that a slow mode falls out of equilibrium if its momentum is greater than a characteristic momentum value. That characteristic momentum turns out to be set by the branch points of the dispersion relations. These branch points occur at the critical momenta of so-called spectral curves and are related to the radius of convergence of the derivative expansion. The existence of such a characteristic momentum scale suggests that a particular class of slow modes has no remarkable effect on the flow of the plasma. Based on these results and previously derived relations to the stiffness of the equation of state, we find a temperature-dependent upper bound for the speed of sound near the critical point in the QCD phase diagram.

arXiv comment36 pages, 13 figures, comments welcome

References in corpus (44)

• Signatures of the Tricritical Point in QCD
• Global $\Lambda$ hyperon polarization in nuclear collisions: evidence for the most vortical fluid
• Mapping the Phases of Quantum Chromodynamics with Beam Energy Scan
• Lectures on hydrodynamic fluctuations in relativistic theories
• Slowing Out of Equilibrium Near the QCD Critical Point
• Hydro+: hydrodynamics with parametric slowing down and fluctuations near the critical point
• Dynamic universality class of the QCD critical point
• Hydrodynamic Fluctuations, Long-time Tails, and Supersymmetry
• The complex life of hydrodynamic modes
• On the convergence of the gradient expansion in hydrodynamics
• Holography and hydrodynamics with weakly broken symmetries
• A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
• Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid
• Theory of diffusive fluctuations
• Relativistic Hydrodynamic Fluctuations
• Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential
• Short-lived modes from hydrodynamic dispersion relations
• Hydro+ in Action: Understanding the Out-of-Equilibrium Dynamics Near a Critical Point in the QCD Phase Diagram
• Fluctuation dynamics in a relativistic fluid with a critical point
• Transits of the QCD Critical Point
• Quasinormal modes in charged fluids at complex momentum
• Stochastic hydrodynamics and long time tails of an expanding conformal charged fluid
• Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field
• Evolution of Non-Gaussian Hydrodynamic Fluctuations
• Hydrodynamic gradient expansion in linear response theory
• Constraints on quasinormal modes and bounds for critical points from pole-skipping
• Critical behavior of the bulk viscosity in QCD
• Convergence of hydrodynamic modes: insights from kinetic theory and holography
• Hydrodynamic diffusion and its breakdown near AdS${}_2$ quantum critical points
• The breakdown of magneto-hydrodynamics near AdS${}_2$ fixed point and energy diffusion bound
• On the universality of AdS${}_2$ diffusion bounds and the breakdown of linearized hydrodynamics
• How small hydrodynamics can go
• Hydrodynamic dispersion relations at finite coupling
• Adding new branches to the "Christmas tree" of the quasinormal spectrum of black branes
• Upper bound of the charge diffusion constant in holography
• Breakdown of hydrodynamics from holographic pole collision
• Relativistic Hydrodynamics: A Singulant Perspective
• Hydrodynamic Gradient Expansion Diverges beyond Bjorken Flow
• The QCD critical point hunt: emergent new ideas and new dynamics
• Critical behaviour of hydrodynamic series
• Collective modes of polarizable holographic media in magnetic fields
• Long-time tails in the SYK chain from the effective field theory with a large number of derivatives
• Relativistic Dynamics of Fluctuations and QCD Critical Point
• Convergence of hydrodynamics in rapidly spinning strongly coupled plasma

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• Hydrodynamic attractors for the speed of sound in holographic Bjorken flow
• Aspects of univalence in holographic axion models