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Spacetime Symmetries from Quantum Er...

Ouseph, Shoy,

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Spacetime Symmetries from Quantum Ergodicity /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Spacetime Symmetries from Quantum Ergodicity // Shoy Ouseph.
Author:	Ouseph, Shoy,
Description:	1 electronic resource (211 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-04, Section: B.
Contained By:	Dissertations Abstracts International86-04B.
Subject:	Thermodynamics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31285326
ISBN:	9798342105873

Spacetime Symmetries from Quantum Ergodicity /
Ouseph, Shoy,

Spacetime Symmetries from Quantum Ergodicity /Shoy Ouseph. - 1 electronic resource (211 pages)

Source: Dissertations Abstracts International, Volume: 86-04, Section: B.

In holographic quantum field theories, a bulk geometric semiclassical spacetime emerges from strongly coupled interacting conformal field theories in one less spatial dimension. This is the celebrated AdS/CFT correspondence. The entanglement entropy of a boundary spatial subregion can be calculated as the area of a codimension two bulk surface homologous to the boundary subregion known as the RT surface. The bulk region contained within the RT surface is known as the entanglement wedge and bulk reconstruction tells us that any operator in the entanglement wedge can be reconstructed as a non-local operator on the corresponding boundary subregion. This notion that entanglement creates geometry is dubbed "ER=EPR'' and has been the driving force behind recent progress in quantum gravity research. In this thesis, we put together two results that use Tomita-Takesaki modular theory and quantum ergodic theory to make progress on contemporary problems in quantum gravity.A version of the black hole information loss paradox is the inconsistency between the decay of two-point functions of probe operators in large AdS black holes and the dual boundary CFT calculation where it is an almost periodic function of time. We show that any von Neumann algebra in a faithful normal state that is quantum strong mixing (two-point functions decay) with respect to its modular flow is a type III 1 factor and the state has a trivial centralizer. In particular, for Generalized Free Fields (GFF) in a thermofield double (KMS) state, we show that if the two-point functions are strong mixing, then the entire algebra is strong mixing and a type III 1factor settling a recent conjecture of Liu and Leutheusser.The semiclassical bulk geometry that emerges in the holographic description is a pseudo-Riemannian manifold and we expect a local approximate Poincare algebra. Near a bifurcate Killing horizon, such a local two-dimensional Poincare algebra is generated by the Killing flow and the outward null translations along the horizon. We show the emergence of such a Poincare algebra in any quantum system with modular future and past subalgebras in a limit analogous to the near-horizon limit. These are known as quantum K-systems and they saturate the modular chaos bound. We also prove that the existence of (modular) future/past von Neumann subalgebras also implies a second law of (modular) thermodynamics.

English

ISBN: 9798342105873Subjects--Topical Terms:

517304
Thermodynamics.

Spacetime Symmetries from Quantum Ergodicity /
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500 $a Source: Dissertations Abstracts International, Volume: 86-04, Section: B.
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502 $b Ph.D. $c Purdue University $d 2024.
520 $a In holographic quantum field theories, a bulk geometric semiclassical spacetime emerges from strongly coupled interacting conformal field theories in one less spatial dimension. This is the celebrated AdS/CFT correspondence. The entanglement entropy of a boundary spatial subregion can be calculated as the area of a codimension two bulk surface homologous to the boundary subregion known as the RT surface. The bulk region contained within the RT surface is known as the entanglement wedge and bulk reconstruction tells us that any operator in the entanglement wedge can be reconstructed as a non-local operator on the corresponding boundary subregion. This notion that entanglement creates geometry is dubbed "ER=EPR'' and has been the driving force behind recent progress in quantum gravity research. In this thesis, we put together two results that use Tomita-Takesaki modular theory and quantum ergodic theory to make progress on contemporary problems in quantum gravity.A version of the black hole information loss paradox is the inconsistency between the decay of two-point functions of probe operators in large AdS black holes and the dual boundary CFT calculation where it is an almost periodic function of time. We show that any von Neumann algebra in a faithful normal state that is quantum strong mixing (two-point functions decay) with respect to its modular flow is a type III 1 factor and the state has a trivial centralizer. In particular, for Generalized Free Fields (GFF) in a thermofield double (KMS) state, we show that if the two-point functions are strong mixing, then the entire algebra is strong mixing and a type III 1factor settling a recent conjecture of Liu and Leutheusser.The semiclassical bulk geometry that emerges in the holographic description is a pseudo-Riemannian manifold and we expect a local approximate Poincare algebra. Near a bifurcate Killing horizon, such a local two-dimensional Poincare algebra is generated by the Killing flow and the outward null translations along the horizon. We show the emergence of such a Poincare algebra in any quantum system with modular future and past subalgebras in a limit analogous to the near-horizon limit. These are known as quantum K-systems and they saturate the modular chaos bound. We also prove that the existence of (modular) future/past von Neumann subalgebras also implies a second law of (modular) thermodynamics.
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