Download PDF by Casalderrey-Solana J., et al.: Gauge-String Duality, Hot QCD and Heavy Ion Collisions

By Casalderrey-Solana J., et al.

ISBN-10: 1107022460

ISBN-13: 9781107022461

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At long enough time scales, however, gradients become unimportant, hydrodynamics becomes ideal, the pressure P in the rest frame of each fluid cell becomes isotropic, and ε and P are related by the equilibrium equation of state. This equation of state can be determined by studying a homogeneous system at rest with no gradients, for example via a lattice calculation. The range of applicability of hydrodynamics can be characterized in terms of the isotropization scale τiso and the hydrodynamization scale τhydro .

21) is such that μν relaxes to its first order form in a (proper) time τ . There are several variants of this equation in the literature, all of which follow the same philosophy. They all introduce the relaxation time as the characteristic time in which the tensor μν relaxes to its first order value. The variations arise from different ways of fixing some pathologies of Eq. 21), since as written Eq. 21) does not lead to a transverse stress tensor (although this is a higher order effect) and is not conformally invariant.

However, there can be other degrees of freedom that lead to long-lived modes in the long wavelength limit. For example, in a phase of matter in which some global symmetry is spontaneously broken, the Goldstone boson(s) is (are) also hydrodynamic modes [355]. The classic example of this is a superfluid, in which a global U (1) symmetry is spontaneously broken. Chiral symmetry is spontaneously broken in QCD, but there are two reasons why we can neglect the potential hydrodynamic modes associated with the chiral order parameter [746].

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Gauge-String Duality, Hot QCD and Heavy Ion Collisions by Casalderrey-Solana J., et al.

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