## 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:

- 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:

- 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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