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Published May 2018 | Published + Submitted
Journal Article Open

Chaos and random matrices in supersymmetric SYK

Abstract

We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary ensemble and compute the spectral form factors and frame potentials to quantify chaos and randomness. Compared to the Gaussian ensembles, we observe the absence of a dip regime in the form factor and a slower approach to Haar-random dynamics. We find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems.

Additional Information

© 2018 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: January 30, 2018; Revised: May 18, 2018; Accepted: May 25, 2018; Published: May 30, 2018. We thank Beni Yoshida for helpful discussions. NHJ acknowledges support from the Simons Foundation through the "It from Qubit" collaboration as well as from the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NSF Grant PHY-1125565) with support from the Gordon and Betty Moore Foundation (GBMF-2644).

Attached Files

Published - 10.1007_2FJHEP05_2018_202.pdf

Submitted - 1710.08184.pdf

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