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Quantum hydrodynamics and the SYK model at next-to-leading order

University of British Columbia

There has been renewed interest in understanding the details and origins of chaos in quantum systems with many degrees of freedom. Chaos plays a significant role in holographic theories, hydrodynamic transport, and even the strange metal phase of condensed matter systems. With this importance, discovering a unified origin that yields universal results for chaotic systems is clearly desirable. In this thesis, we investigate the conjectured hydrodynamic origin of quantum many-body chaos, first posited in [1], by testing it with the next-to-leading order SYK model. We provide a review of how hydrodynamic theories are constructed, and how hydrodynamic theories with a certain symmetry possess all the standard features of chaos. We then review the leading order SYK model, demonstrate its chaotic behaviour, and compare it with the predictions of the hydrodynamic theory. We finally perform an in-depth investigation of the next-to-leading order SYK model, demonstrating that, while one sector of the theory satisfies the conjecture, another sector does not admit a hydrodynamic description. This shows that the conjecture must be modified to account for near-maximally chaotic theories.

Text

2019-04-24

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69904

Physics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/