Chaos and random matrices in supersymmetric SYK

doi:10.1007/jhep05(2018)202

Title: Chaos and random matrices in supersymmetric SYK

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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:

^[1]; Liu, Junyu ^[2]

California Inst. of Technology (CalTech), Pasadena, CA (United States). Institute for Quantum Information and Matter
California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics

Publication Date:: 2018-05-30

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.

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                    Hunter-Jones, Nicholas, & Liu, Junyu. Chaos and random matrices in supersymmetric SYK.  United States.  doi:10.1007/jhep05(2018)202.

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                    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.

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@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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