Using the AdS/CFT correspondence, we probe the scale-dependence of thermalization in strongly coupled field theories following a sudden injection of energy, via calculations of two-point functions, Wilson loops and entanglement entropy in d = 2, 3, 4. In the saddlepoint approximation these probes are computed in AdS space in terms of invariant geometric objects -geodesics, minimal surfaces and minimal volumes. Our calculations for two-dimensional field theories are analytical. In our strongly coupled setting, all probes in all dimensions share certain universal features in their thermalization: (1) a slight delay in the onset of thermalization, (2) an apparent non-analyticity at the endpoint of thermalization, (3) top-down thermalization where the UV thermalizes first. For homogeneous initial conditions the entanglement entropy thermalizes slowest, and sets a timescale for equilibration that saturates a causality bound over the range of scales studied. The growth rate of entanglement entropy density is nearly volume-independent for small volumes, but slows for larger volumes.
Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in 2, 3, and 4 dimensions to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest, and sets a timescale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volumeindependent for small volumes, but slows for larger volumes. In this setting, the UV thermalizes first.
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