Phase Transitions and the Perfectness of Fluids

Journal of High Energy Physics, 2012

We examine the structure of the shear viscosity to entropy density ratio η s in holographic theories of gravity coupled to a scalar field, in the presence of higher derivative corrections. Thanks to a non-trivial scalar field profile, η s in this setup generically runs as a function of temperature. In particular, its temperature behavior is dictated by the shape of the scalar potential and of the scalar couplings to the higher derivative terms. We consider a number of dilatonic setups, but focus mostly on phenomenological models that are QCD-like. We determine the geometric conditions needed to identify local and global minima for η s as a function of temperature, which translate to restrictions on the signs and ranges of the higher derivative couplings. Finally, such restrictions lead to an holographic argument for the existence of a global minimum for η s in these models, at or above the deconfinement transition.

Physical Review C, 2008

We solve the relativistic Navier-Stokes equations with homogeneous boost-invariant boundary conditions, and perform a stability analysis of the solution. We show that, if the bulk viscosity has a peak around Tc as inferred from QCD-based arguments, the background solution "freezes" at Tc to a nearly constant temperature state. This state is however highly unstable with respect to certain inhomogeneous modes. Calculations show that these modes have enough time to blow up and tear the system into droplets. We conjecture that this is how freeze-out occurs in the QGP created in heavy ion collisions, and perhaps similar transitions in the early universe. PACS numbers: 25.75.-q,25.75.Dw,25.75.Nq

Physical Review C, 2009

In this work, we examine the effect of bulk viscosity on elliptic flow taking into account the critical behavior of the EoS and transport coefficients near the QCD phase transition. We found that the pT dependence of v2 is quantitatively changed by the presence of the QCD phase transition. Within reasonable values of the transport coefficients, v2 decreases by a factor of 15% at low pT (< 1 GeV). However, for larger values of pT (> 2 GeV), the interplay between the velocity of sound and transport coefficient near the QCD phase transition enhances v2. We further point out that Grad's 14 moments approximation cannot be applied for the calculation of the one-particle distribution function at the freeze-out.

2015

Eighty years ago Eyring proposed that the shear viscosity of a liquid, η, has a quantum limit η n where n is the density of the fluid. Using holographic duality and the AdS/CFT correspondence in string theory Kovtun, Son, and Starinets (KSS) conjectured a universal bound η s ≥ 4πk B for the ratio between the shear viscosity and the entropy density, s. Using Dynamical Mean-Field Theory (DMFT) we calculate the shear viscosity and entropy density for a fermionic fluid described by a single band Hubbard model at half filling. Our calculated shear viscosity as a function of temperature is compared with experimental data for liquid 3 He. At low temperature the shear viscosity is found to be well above the quantum limit and is proportional to the characteristic Fermi liquid 1/T 2 dependence, where T is the temperature. With increasing temperature and interaction strength U there is significant deviation from the Fermi liquid form. Also, the shear viscosity violates the quantum limit near the crossover from coherent quasi-particle based transport to incoherent transport (the bad metal regime). Finally, the ratio of the shear viscosity to the entropy density is found to be comparable to the KSS bound for parameters appropriate to liquid 3 He. However, this bound is found to be strongly violated in the bad metal regime for parameters appropriate to lattice electronic systems such as organic charge transfer salts.

2009

In this work, we examine the effect of bulk viscosity on elliptic flow taking into account the critical behavior of the EoS and transport coefficients near the QCD phase transition. We found that the pT dependence of v2 is quantitatively changed by the presence of the QCD phase transition. Within reasonable values of the transport coefficients, v2 decreases by a factor of 15% at low pT (< 1 GeV). However, for larger values of pT (> 2 GeV), the interplay between the velocity of sound and transport coefficient near the QCD phase transition enhances v2. We further point out that Grad's 14 moments approximation cannot be applied for the calculation of the one-particle distribution function at the freeze-out.

Physics Letters A, 2009

Starting from relativistic quantum field theories, have quite recently proposed a lower bound η/s ≥ /(4πk B ), where η is the shear viscosity and s the volume density of entropy for dense liquids. If their proposal can eventually be proved, then this would provide key theoretical underpinning to earlier semiempirical proposals on the relation between a transport coefficient η and a thermodynamic quantity s. Here, we examine largely experimental data on some dense liquids, the insulators nitrogen, water, and ammonia, plus the alkali metals, where the shear viscosity η(T ) for the four heaviest alkalis is known to scale onto an 'almost universal' curve, following the work of Tankeshwar and March a decade ago. So far, all known results for both insulating and metallic dense liquids correctly exceed the lower bound prediction of Kovtun et al.

Physical Review Letters, 1999

1999

We review the formalism of the effective average action in quantum field theory which corresponds to a coarse grained free energy in statistical mechanics. The associated exact renormalization group equation and possible nonperturbative approximations for its solution are discussed. We describe in detail O(N)-symmetric scalar theories in two and three dimensions. These ideas are also applied to QCD where one observes the consecutive emergence of mesonic bound states and spontaneous chiral symmetry breaking as the coarse graining scale is lowered. We finally present a study of the chiral phase transition in two flavor QCD. A precision estimate of the universal critical equation of state for the three-dimensional O(4) Heisenberg model is presented. We explicitly connect the O(4) universal behavior near the critical temperature and zero quark mass with the physics at zero temperature and a realistic pion mass. For realistic quark masses the pion correlation length near T_c turns out to be smaller than its zero temperature value.

Physical Review D, 1996

In this paper we study the statistical mechanics of the instanton liquid in QCD. After introducing the partition function as well as the gauge field and quark induced interactions between instantons we describe a method to calculate the free energy of the instanton system. We use this method to determine the equilibrium density and the equation of state from numerical simulations of the instanton ensemble in QCD for various numbers of flavors. We find that there is a critical number of flavors above which chiral symmetry is restored in the groundstate. In the physical case of two light and one intermediate mass flavor the system undergoes a chiral phase transition at T ≃ 140 MeV. We show that the mechanism for this transition is a rearrangement of the instanton liquid, going from a disordered, random, phase at low temperatures to a strongly correlated, molecular, phase at high temperature. We also study the behavior of mesonic susceptibilities near the phase transition.

Journal of Physics G: Nuclear and Particle Physics, 2017

The bulk viscosity (ζ) of the hadronic medium has been estimated within the ambit of the Hadron Resonance Gas (HRG) model including the Hagedorn density of states. The HRG thermodynamics within a grand canonical ensemble provides the mean hadron number as well as its fluctuation. The fluctuation in the chemical composition of the hadronic medium in the grand canonical ensemble can result in non-zero divergence of the hadronic fluid flow velocity, allowing us to estimate the ζ of the hadronic matter upto a relaxation time. We study the influence of the hadronic spectrum on ζ and find its correlation with the conformal symmetry breaking (CSB) measure, − 3P. We estimate ζ along the contours with constant, S/N B (total entropy/net baryon number) in the T − µ plane (temperature-baryonic chemical potential) for S/N B = 30, 45 and 300. We also assess the value of ζ on the chemical freezeout curve for various centre of mass energy (√ s N N) and find that the bulk viscosity to entropy density ratio, ζ/s is larger at FAIR than LHC energies.