Spectral form factors and late time quantum chaos

Liu, Junyu

doi:10.1103/PhysRevD.98.086026

Title: Spectral form factors and late time quantum chaos

Abstract

This is a collection of notes about spectral form factors of standard ensembles in random matrix theory, written for the practical usage of the current study of late time quantum chaos. More precisely, we consider the Gaussian unitary ensemble, the Gaussian orthogonal ensemble, the Gaussian symplectic ensemble, the Wishart-Laguerre unitary ensemble, the Wishart-Laguerre orthogonal ensemble, and the Wishart-Laguerre symplectic ensemble. These results and their physics applications cover a threefold classification of late time quantum chaos in terms of spectral form factors.

Authors:

Liu, Junyu ^[1]

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

Publication Date:: Wed Oct 31 00:00:00 EDT 2018

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1599631

Grant/Contract Number:: SC0011632

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 98; Journal Issue: 8; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Liu, Junyu. Spectral form factors and late time quantum chaos.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevD.98.086026.

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                    Liu, Junyu. Spectral form factors and late time quantum chaos.  United States.  https://doi.org/10.1103/PhysRevD.98.086026

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                    Liu, Junyu. Wed .  
"Spectral form factors and late time quantum chaos".  United States.  https://doi.org/10.1103/PhysRevD.98.086026.  https://www.osti.gov/servlets/purl/1599631.

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@article{osti_1599631,

  title        = {Spectral form factors and late time quantum chaos},

  author       = {Liu, Junyu},

  abstractNote = {This is a collection of notes about spectral form factors of standard ensembles in random matrix theory, written for the practical usage of the current study of late time quantum chaos. More precisely, we consider the Gaussian unitary ensemble, the Gaussian orthogonal ensemble, the Gaussian symplectic ensemble, the Wishart-Laguerre unitary ensemble, the Wishart-Laguerre orthogonal ensemble, and the Wishart-Laguerre symplectic ensemble. These results and their physics applications cover a threefold classification of late time quantum chaos in terms of spectral form factors.},

  doi          = {10.1103/PhysRevD.98.086026},

  journal      = {Physical Review D},

  number       = 8,

  volume       = 98,

  place        = {United States},

  year         = {Wed Oct 31 00:00:00 EDT 2018},

  month        = {Wed Oct 31 00:00:00 EDT 2018}

}

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Works referenced in this record:

Universal spectral correlations in the chaotic wave function and the development of quantum chaos
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Chen, Xiao; Ludwig, Andreas W. W.
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Chaos and complexity by design
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A bound on chaos
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Complete random matrix classification of SYK models with N $$ \mathcal{N} $$ = 0, 1 and 2 supersymmetry
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Kanazawa, Takuya; Wettig, Tilo
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Supersymmetric SYK model and random matrix theory
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Li, Tianlin; Liu, Junyu; Xin, Yuan
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Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu
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Black holes and the butterfly effect
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Fast scramblers
journal, October 2008

Sekino, Yasuhiro; Susskind, L.
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Stringy effects in scrambling
journal, May 2015

Shenker, Stephen H.; Stanford, Douglas
Journal of High Energy Physics, Vol. 2015, Issue 5
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Sachdev-Ye-Kitaev model and thermalization on the boundary of many-body localized fermionic symmetry-protected topological states
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Physical Review B, Vol. 95, Issue 11
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Chaos and random matrices in supersymmetric SYK
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Works referencing / citing this record:

Eigenvalue instantons in the spectral form factor of random matrix model
journal, March 2019

Okuyama, Kazumi
Journal of High Energy Physics, Vol. 2019, Issue 3
DOI: 10.1007/jhep03(2019)147

Eigenvalue instantons in the spectral form factor of random matrix model
text, January 2018

Okuyama, Kazumi
arXiv
DOI: 10.48550/arxiv.1812.09469

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Similar Records

Title: Spectral form factors and late time quantum chaos

Abstract

Citation Formats

Universal spectral correlations in the chaotic wave function and the development of quantum chaos journal, August 2018

Onset of random matrix behavior in scrambling systems journal, July 2018

Black holes as mirrors: quantum information in random subsystems journal, September 2007

Towards the fast scrambling conjecture journal, April 2013

Chaos and complexity by design journal, April 2017

A bound on chaos journal, August 2016

Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model journal, December 2016

Complete random matrix classification of SYK models with N $$ \mathcal{N} $$ = 0, 1 and 2 supersymmetry journal, September 2017

Supersymmetric SYK model and random matrix theory journal, June 2017

Chaos, complexity, and random matrices journal, November 2017

Black holes and the butterfly effect journal, March 2014

Fast scramblers journal, October 2008

Stringy effects in scrambling journal, May 2015

Sachdev-Ye-Kitaev model and thermalization on the boundary of many-body localized fermionic symmetry-protected topological states journal, March 2017

Chaos and random matrices in supersymmetric SYK journal, May 2018

Characteristic Vectors of Bordered Matrices With Infinite Dimensions journal, November 1955

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Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws journal, January 1984

Riemannian symmetric superspaces and their origin in random‐matrix theory journal, October 1996

Eigenvalue instantons in the spectral form factor of random matrix model journal, March 2019

Eigenvalue instantons in the spectral form factor of random matrix model text, January 2018

Universal spectral correlations in the chaotic wave function and the development of quantum chaos
journal, August 2018

Onset of random matrix behavior in scrambling systems
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Black holes as mirrors: quantum information in random subsystems
journal, September 2007

Towards the fast scrambling conjecture
journal, April 2013

Chaos and complexity by design
journal, April 2017

A bound on chaos
journal, August 2016

Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
journal, December 2016

Complete random matrix classification of SYK models with N $$ \mathcal{N} $$ = 0, 1 and 2 supersymmetry
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Supersymmetric SYK model and random matrix theory
journal, June 2017

Chaos, complexity, and random matrices
journal, November 2017

Black holes and the butterfly effect
journal, March 2014

Fast scramblers
journal, October 2008

Stringy effects in scrambling
journal, May 2015

Sachdev-Ye-Kitaev model and thermalization on the boundary of many-body localized fermionic symmetry-protected topological states
journal, March 2017

Chaos and random matrices in supersymmetric SYK
journal, May 2018

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