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We describe the application of pseudo-spectral methods to problems ofholographic thermal quenches of relevant couplings in strongly coupled gaugetheories. We focus on quenches of a fermionic mass term in a strongly coupledN=4 supersymmetric Yang-Mills plasma, and the subsequent equilibration of thesystem. From the dual gravitational perspective, we study the gravitationalcollapse of a massive scalar field in asymptotically anti-de Sitter geometrywith a prescribed boundary condition for its non-normalizable mode. Access tothe full background geometry of the gravitational collapse allows for the studyof nonlocal probes of the thermalization process. We discuss the evolution ofthe apparent and the event horizons, the two-point correlation functions ofoperators of large conformal dimensions, and the evolution of the entanglemententropy of the system. We compare the thermalization process from the viewpointof local (the one-point) correlation functions and these nonlocal probes,finding that the thermalization time as measured by the probes is lengthdependent, and approaches the thermalization time of the one-point function forlonger probes. We further discuss how the different energy scales of theproblem contribute to its thermalization.

Nonlocal probes of thermalization in holographic quenches with spectral methods