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Title: 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. Here we find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems.

Authors:
ORCiD logo [1];  [2]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States). Institute for Quantum Information and Matter
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
Publication Date:
Research Org.:
California Inst. of Technology, Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1501440
Grant/Contract Number:  
SC0011632
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 5; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 2D Gravity; AdS-CFT Correspondence; Matrix Models; Random Systems

Citation Formats

Hunter-Jones, Nicholas, and Liu, Junyu. Chaos and random matrices in supersymmetric SYK. United States: N. p., 2018. Web. doi:10.1007/jhep05(2018)202.
Hunter-Jones, Nicholas, & Liu, Junyu. Chaos and random matrices in supersymmetric SYK. United States. doi:10.1007/jhep05(2018)202.
Hunter-Jones, Nicholas, and Liu, Junyu. Wed . "Chaos and random matrices in supersymmetric SYK". United States. doi:10.1007/jhep05(2018)202. https://www.osti.gov/servlets/purl/1501440.
@article{osti_1501440,
title = {Chaos and random matrices in supersymmetric SYK},
author = {Hunter-Jones, Nicholas and Liu, Junyu},
abstractNote = {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. Here we find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems.},
doi = {10.1007/jhep05(2018)202},
journal = {Journal of High Energy Physics (Online)},
number = 5,
volume = 2018,
place = {United States},
year = {2018},
month = {5}
}

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