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Equilibration Mechanisms in Weakly and Strongly Coupled Quantum Field Theory (INT-15-2c)
(INT Program August 3 - 28, 2015)

Reported by Jorge Casalderrey Solana, Francois Gelis, Aleksi Kurkela, Aleksi Vuorinen
  Date posted September 28, 2015

"Holography and off-center collisions of localized shock waves", P.M. Chesler and L.G. Yaffe, ARXIV:1501.04644

The out-of-equilibrium dynamics of systems described by quantum field theory is a notoriously complicated topic that has witnessed a renewed interest during the past decade. Although this has mostly stemmed from the physics of heavy ion collisions, further applications to systems ranging from the reheating of the early universe to quantum quenches in condensed matter systems have been widely discussed as well. In the field of heavy ion collisions, relativistic hydrodynamics is used in most phenomenological studies of the bulk evolution of the system, and leads to a very successful description of many experimental measurements. However, understanding from first principles (i.e. in terms of the underlying quantum field theory) why a small system of quarks and gluons may be amenable to a such description has been rather elusive so far.

Recent progress in the field has been largely due to two independent developments. First, work on weakly coupled methods including simulations of classical Yang-Mills theory on the lattice and a reformulation of perturbation theory in form of effective kinetic theory have significantly increased our understanding of the approach to equilibrium of many different systems of increasing complexity. Secondly, at the same time a parallel development in the gauge/gravity duality has enabled mapping the strong coupling equilibration process to black hole formation in General Relativity, which by itself is a challenging, but significantly more manageable problem to tackle.

Our program on equilibration mechanisms in quantum field theory aimed at bringing together experts working on out-of-equilibrium problems with a broad range of approaches and tools. This resulted in very lively (and sometimes vigorous) discussions, with new collaborations emerging both within and between the different sub-communities. Below, we provide a few examples of recent research highlights that were presented and actively discussed at the workshop:

  1. Simulations of systems that mimic heavy ion collisions - and the subsequent equilibration process - using strongly coupled N=4 Super Yang-Mills theory have recently reached a state where collisions of bounded and localized shock waves at nonzero impact parameter can be quantitatively studied. In the included figure, taken from [CherlerYaffe], we observe the energy density and energy flux in such a system at four different times, in coordinates where the shock waves move along the z direction. The emergence of transverse flow is clearly visible in the figure.

  2. Several attempts to take applications of the holograpic duality away from the usual limit of infinitely strongly coupled supersymmetric conformal field theories were reported in the program, covering both equilibrium physics and thermalization. Recent progress includes both inclusion of finite-coupling corrections to transport coefficients and quasinormal modes, as well as studies of shock wave collisions in a conformality-breaking background. Such developments are crucial in order to assess the degree of universality of the numerous existing analyses of holographic thermalization.

  3. Another major thread of recent works on thermalization is based on lattice simulations of classical Yang-Mills equations. This approach assumes weak coupling, and uses the resulting large gluon occupation number to simplify the dynamics of the system into a classical evolution, which is possible to implement in numerical simulations. Weakly coupled but highly occupied (with bosonic occupation numbers proportional to the inverse coupling) systems have in fact some resemblance with strongly coupled systems in the sense that the leading order results are independent of the coupling. Such systems may be viewed as weakly coupled but nevertheless strongly interacting.

  4. While classical Yang-Mills theory methods are restricted to over-occupied systems and therefore can never reach thermal equilibrium, effective kinetic theory methods have no problem reaching the equilibrium state and allow to fully take into account quantum effects. For occupancies which are high but non-perturbative it has been shown that both formulations give an equivalently good description. Therefore a combination of classical and kinetic theory methods can now be used to follow the pre-equilibrium evolution at weak coupling all the way from a over-occupied initial condition all the way to local thermal equilibrium.

  5. In addition to studies of the thermalization process, a lot of attention has been placed to trying to understand the limitations of the applicability of hydrodynamics, and in particular how the current situation could be improved. The roles of quasinormal modes and the convergence of the gradient expansion in this were discussed, and several talks given about an alternative hydrodynamic expansion around an anisotropic background.