Title: Entanglement entropy from numerical holography
Language: English
Authors: Ecker, Christian 
Qualification level: Doctoral
Advisor: Grumiller, Daniel 
Assisting Advisor: Rebhan, Anton 
Issue Date: 2018
Ecker, C. (2018). Entanglement entropy from numerical holography [Dissertation, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2018.29585
Number of Pages: 136
Qualification level: Doctoral
siehe eng.

In this thesis I present numerical studies of entanglement entropy and the quantum null energy condition in strongly coupled far-from-equilibrium quantum states using holography. The holographic prescription for entanglement entropy requires to determine the area of extremal surfaces in asymptoticaly Anti-de Sitter spacetimes which I do both numerically and, when possible, analytically. I give a careful introduction into the numerical methods used and provide the computer codes to compute entanglement entropy and the quantum null energy condition. These methods are then applied to systems of various degrees of complexity, including homogeneous and isotropic far-from-equilibrium quantum quenches dual to Vaidya spacetimes, to homogeneous and anisotropic finite temperature states dual to anisotropic black brane geometries, and to inhomogeneous and anisotropic states of colliding walls of energy dual to gravitational shock wave collisions in Anti-de Sitter space. For all these scenarios I compute the fully non-linear dynamics of the dual geometry, which requires to numerically solve five-dimensional Einstein equations with negative cosmological constant and asymptotic Anti-de Sitter boundary conditions. The numerical solutions for the geometries allow to extract the time evolution of the holographic energy momentum tensor and provides the background for computing two-point functions, entanglement entropy and the quantum null energy condition. From the anisotropic system one learns that the near-equilibrium dynamic of entanglement entropy has an accurate description in terms of quasinormal modes. In the shock wave system I identify characteristic features of entanglement entropy that allow to discriminate between thick and narrow shocks. All my numerical studies confirm the quantum null energy condition, also the shock wave system, which itself can violate the classical null energy condition for sufficiently narrow shocks. My results also show that the quantum null energy condition can saturate in the far-from-equilibrium regime.
Keywords: entanglement entropy; holography; AdS; CFT correspondence; quantum null energy condition; numerical relativity
URI: https://doi.org/10.34726/hss.2018.29585
DOI: 10.34726/hss.2018.29585
Library ID: AC15151561
Organisation: E136 - Institut für Theoretische Physik 
Publication Type: Thesis
Appears in Collections:Thesis

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