Abstract
We describe the application of pseudo-spectral methods to problems of holographic thermal quenches of relevant couplings in strongly coupled gauge theories. We focus on quenches of a fermionic mass term in a strongly coupled N=4 supersymmetric Yang-Mills plasma, and the subsequent equilibration of the system. From the dual gravitational perspective, we study the gravitational collapse of a massive scalar field in asymptotically anti-de Sitter geometry with a prescribed boundary condition for its non-normalizable mode. Access to the full background geometry of the gravitational collapse allows for the study of nonlocal probes of the thermalization process. We discuss the evolution of the apparent and the event horizons, the two-point correlation functions of operators of large conformal dimensions, and the evolution of the entanglement entropy of the system. We compare the thermalization process from the viewpoint of local (the one-point) correlation functions and these nonlocal probes, finding that the thermalization time as measured by the probes is length dependent, and approaches the thermalization time of the one-point function for longer probes. We further discuss how the different energy scales of the problem contribute to its thermalization.
Highlights
Quantum quenches are processes where an isolated system is driven to a far-fromequilibrium state by rapidly varying some control parameters
Access to the full background geometry of the gravitational collapse allows for the study of nonlocal probes of the thermalization process
The main challenge is that gravitational simulations in asymptotically Minkowski spacetimes mostly have a compact physical dependence domain; on the contrary, in AdS, control over the whole spacetime, and especially near the boundary is crucial. The latter is emphasized in problems related to holographic quenches, where the temporal history of a quantum gauge theory coupling is encoded as a non-normalizable component of the gravitationally dual bulk scalar field near the boundary
Summary
Quantum quenches are processes where an isolated system is driven to a far-fromequilibrium state by rapidly varying some control parameters. In an ongoing research program including [51, 52] and [53], we study the response of a strongly coupled N = 4 supersymmetric Yang-Mills thermal plasma, quenched by a relevant operator, using the holographic duality Having previously studied such quenches, we apply more powerful numerical techniques to find the full time-dependent profiles of the perturbations of the metric and scalar field in the dual AdS spacetime. This allows us to utilize nonlocal probes such as two-point functions and entanglement entropy to better understand thermalization at various distance scales. This will serve as a prelude to the new solution of the full non-perturbative backreaction of the scalar field on the AdS-black brane geometry
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