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Chaos and Randomness in Strongly-Interacting Quantum Systems


Hunter-Jones, Nicholas R. (2018) Chaos and Randomness in Strongly-Interacting Quantum Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/BHZ5-HV76.


Quantum chaos entails an entropic and computational obstruction to describing a system and thus is intrinsically difficult to characterize. An understanding of quantum chaos is fundamentally related to the mechanism of thermalization in many-body systems and the quantum nature of black holes. In this thesis we adopt the view that quantum information theory provides a powerful framework in which to elucidate chaos in strongly-interacting quantum systems.

We first push towards a more precise understanding of chaotic dynamics by relating different diagnostics of chaos, studying the time-evolution of random matrix Hamiltonians, and quantifying random matrix behavior in physical systems. We derive relations between out-of-time ordered correlation functions, spectral quantities, and frame potentials to relate the scrambling of quantum information, decay of correlators, and Haar-randomness. We give analytic expressions for these quantities in random matrix theory to explore universal aspects of late-time dynamics. Motivated by our random matrix results, we define k-invariance in order to capture the onset of random matrix behavior in physical systems.

We then refine our diagnostics in order to study chaotic systems with symmetry by considering Haar-randomness with respect to quotients of the unitary group, and in doing so we generalize our quantum information machinery. We further consider extended random matrix ensembles in the context of strongly-interacting quantum systems dual to black holes. Lastly, we study operator growth in classes of random quantum circuits.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Quantum chaos; scrambling; black holes; random matrix theory; strongly-interacting systems
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Preskill, John P.
Group:Institute for Quantum Information and Matter
Thesis Committee:
  • Preskill, John P. (chair)
  • Kitaev, Alexei
  • Brandao, Fernando
  • Simmons-Duffin, David
Defense Date:22 May 2018
Funding AgencyGrant Number
Simons Foundation'It from Qubit' collaboration
Department of Energy (DOE)DE-SC0018407
National Science Foundation (NSF)PHY-1125565
Gordon and Betty Moore FoundationGBMF-2644
Record Number:CaltechTHESIS:06012018-143029746
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Ch. 2 adapted for Ch. 4
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11002
Deposited By: Nicholas Hunter-Jones
Deposited On:04 Jun 2018 21:15
Last Modified:08 Aug 2022 17:49

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