Within a holographic model, we calculate the time evolution of 2-point and 1point correlation functions (of selected operators) within a charged strongly coupled system of many particles. That system is thermalizing from an anisotropic initial charged state far from equilibrium towards equilibrium while subjected to a constant external magnetic field. One main result is that thermalization times for 2-point functions are significantly (approximately three times) larger than those of 1-point functions. Magnetic field and charge amplify this difference, generally increasing thermalization times. However, there is also a competition of scales between charge density, magnetic field, and initial anisotropy, which leads to an array of qualitative changes on the 2-and 1-point functions. There appears to be a strong effect of the medium on 2-point functions at early times, but approximately none at later times. At strong magnetic fields, an apparently universal thermalization time emerges, at which all 2-point functions appear to thermalize regardless of any other scale in the system. Hence, this time scale is referred to as saturation time scale. As extremality is approached in the purely charged case, 2-and 1-point functions appear to equilibrate at infinitely late time. We also compute 2-point functions of charged operators. Our results can be taken to model thermalization in heavy ion collisions, or thermalization in selected condensed matter systems.
We report analytically known states at non-zero temperature which may serve as a powerful tool to reveal common topological and thermodynamic properties of systems ranging from the QCD phase diagram to topological phase transitions in condensed matter materials. In the holographically dual gravity theory, these are analytic solutions to a five-dimensional non-linear-sigma (Skyrme) model dynamically coupled to Einstein gravity. This theory is shown to be holographically dual to $$ \mathcal{N} $$
N
= 4 Super-Yang-Mills theory coupled to an SU(2)-current. All solutions are fully backreacted asymptotically Anti-de Sitter (AdS) black branes or holes. One family of global AdS black hole solutions contains non-Abelian gauge field configurations with positive integer Chern numbers and finite energy density. Larger Chern numbers increase the Hawking-Page transition temperature. In the holographically dual field theory this indicates a significant effect on the deconfinement phase transition. Black holes with one Hawking temperature can have distinct Chern numbers, potentially enabling topological transitions. A second family of analytic solutions, rotating black branes, is also provided. These rotating solutions induce states with propagating charge density waves in the dual field theory. We compute the Hawking temperature, entropy density, angular velocity and free energy for these black holes/branes. These correspond to thermodynamic data in the dual field theory. For these states the energy-momentum tensor, (non-)conserved current, and topological charge are interpreted.
We report on the time evolution of a charged strongly coupled N = 4 SYM plasma with an axial anomaly subjected to strong electromagnetic fields. The evolution of this plasma corresponds to a fully backreacted asymptotically AdS5 solution to the Einstein-Maxwell-Chern-Simons theory. We explore the evolution of the axial current and production of axial charges. As an application we show that after a sufficiently long time both the entropy and the holographic entanglement entropy of a strip-like topology (both parallel to and transverse to the flow of axial current) grow linearly in time.
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