Abstract
We present a direct comparison studying equilibration through kinetic theory at weak coupling and through holography at strong coupling in the same set-up. The set-up starts with a homogeneous thermal state, which then smoothly transitions through an out-of-equilibrium phase to an expanding system undergoing boost-invariant flow. This first apples-to-apples comparison of equilibration provides a benchmark for similar equilibration processes in heavy-ion collisions, where the equilibration mechanism is still under debate. We find that results at weak and strong coupling can be smoothly connected by simple, empirical power-laws for the viscosity, equilibration time and entropy production of the system.
Highlights
On the other hand, equilibration at strong coupling has been studied using the gauge/ gravity duality or holography [33], in which it is remarkably straightforward to study real time dynamics for certain gauge theories
The initial condition of the pre-equilibrium evolution at weak coupling is usually described in terms of classical fields or distribution functions whereas at strong coupling the initial condition has to be formulated in terms of fields in AdS space-time
For λ = ∞, the system is described by hydrodynamics very quickly after the pulse has ended, but the departure from equilibrium does leave an imprint in non-equilibrium entropy production
Summary
We consider a gauge theory initially in global equilibrium at the temperature Ti. With g(t) a function that smoothly transitions from g(t → −∞) = 1 to g(t → ∞) → t2 at late times t This choice of metric tensor implies that for t → −∞, the gauge theory is in global equilibrium at rest within a flat space-time, as outlined above. The most general stress tensor complete up to second order gradients in arbitrary d-dimensional space-times is given by [50]. For the line element (2.1), with the initial condition of global equilibrium at temperature Ti, one finds that the fluid dynamic solution maintains the initial condition of vanishing spatial flow velocity, so that uμ = (1, 0) This implies = −Ttt, and effective transverse and longitudinal pressures of. Going beyond Navier-Stokes, for the BRSSS equations it will be useful to define the common parametrizations τπ
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