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J. L. F. Barbón, E. Rabinovici, R. Shir and R. Sinha, “On The Evolution Of Operator Complexity Beyond Scrambling,” JHEP 10
Original
1907
Earlier work this paper cites.
P. Saad, “Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity,” [arXiv:1910.10311 [hep-th]]
Original
1910
Earlier work this paper cites.
M. Srednicki, “The approach to thermal equilibrium in quantized chaotic systems,” J. Phys. A 32
1999
Earlier work this paper cites.
S. Lloyd, “Ultimate Physical limits to computation,” Nature 406
2000
Earlier work this paper cites.
M. L. Mehta,“ Random Matrices.” (Elsevier, San Diego, 2004) Third edition
2004
Earlier work this paper cites.
S. K. Jian, B. Swingle and Z. Y. Xian, “Complexity growth of operators in the SYK model and in JT gravity,” JHEP 03
Original
2008
Earlier work this paper cites.
E. Rabinovici, A. Sánchez-Garrido, R. Shir and J. Sonner, “Operator complexity: a journey to the edge of Krylov space,” JHEP 06
Original
2009
Earlier work this paper cites.
L. Susskind, “Computational Complexity and Black Hole Horizons,” Fortsch. Phys. 64
Original
2016
Earlier work this paper cites.

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L. Susskind, “Entanglement is not enough,” Fortsch. Phys. 64
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L. D’Alessio, Y. Kafri, A. Polkovnikov and M. Rigol, “From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics,” Adv. Phys. 65
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D. Bagrets, A. Altland and A. Kamenev, “Sachdev–Ye–Kitaev model as Liouville quantum mechanics,” Nucl. Phys. B 911
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A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Holographic Complexity Equals Bulk Action?,” Phys. Rev. Lett. 116
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Z. Yang, “The Quantum Gravity Dynamics of Near Extremal Black Holes,” JHEP 05

Then

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2022

On Quantum Complexity

Alishahiha, Mohsen

Understand

The ETH ansatz for matrix elements of a given operator in the energy eigenstate basis results in a notion of thermalization for a chaotic system.

In this context for a certain quantity - to be found for a given model - one may impose a particular condition on its matrix elements in the energy eigenstate basis so that the corresponding quantity exhibit linear growth at late times.
The condition is to do with a possible pole structure the corresponding matrix elements may have.
Based on the general expectation of complexity one may want to think of this quantity as a possible candidate for the quantum complexity.

Built on

J. L. F. Barbón, E. Rabinovici, R. Shir and R. Sinha, “On The Evolution Of Operator Complexity Beyond Scrambling,” JHEP 10
Original
1907
Earlier work this paper cites.
P. Saad, “Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity,” [arXiv:1910.10311 [hep-th]]
Original
1910
Earlier work this paper cites.
M. Srednicki, “The approach to thermal equilibrium in quantized chaotic systems,” J. Phys. A 32
1999
Earlier work this paper cites.
S. Lloyd, “Ultimate Physical limits to computation,” Nature 406
2000
Earlier work this paper cites.
M. L. Mehta,“ Random Matrices.” (Elsevier, San Diego, 2004) Third edition
2004
Earlier work this paper cites.
S. K. Jian, B. Swingle and Z. Y. Xian, “Complexity growth of operators in the SYK model and in JT gravity,” JHEP 03
Original
2008
Earlier work this paper cites.
E. Rabinovici, A. Sánchez-Garrido, R. Shir and J. Sonner, “Operator complexity: a journey to the edge of Krylov space,” JHEP 06
Original
2009
Earlier work this paper cites.
L. Susskind, “Computational Complexity and Black Hole Horizons,” Fortsch. Phys. 64
Original
2016
Earlier work this paper cites.

Similar

L. Susskind, “Entanglement is not enough,” Fortsch. Phys. 64
Original
2016
Cited alongside, same era.
L. D’Alessio, Y. Kafri, A. Polkovnikov and M. Rigol, “From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics,” Adv. Phys. 65
Original
2016
Cited alongside, same era.
D. Bagrets, A. Altland and A. Kamenev, “Sachdev–Ye–Kitaev model as Liouville quantum mechanics,” Nucl. Phys. B 911
Original
2016
Cited alongside, same era.
A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Holographic Complexity Equals Bulk Action?,” Phys. Rev. Lett. 116
Original
2016
Cited alongside, same era.
Z. Yang, “The Quantum Gravity Dynamics of Near Extremal Black Holes,” JHEP 05

Then

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2019

Cited alongside, same era.

D. E. Parker, X. Cao, A. Avdoshkin, T. Scaffidi and E. Altman, “A Universal Operator Growth Hypothesis,” Phys. Rev. X 9

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2019

Cited alongside, same era.

D. Harlow and D. Jafferis, “The Factorization Problem in Jackiw-Teitelboim Gravity,” JHEP 02

Original

2020

Cited alongside, same era.

M. Srednicki, “Chaos and Quantum Thermalization,” doi:10.1103/PhysRevE.50.888 [arXiv:cond-mat/9403051 [cond-mat]]

Cited in the paper.

M. Alishahiha and S. Banerjee, “A universal approach to Krylov State and Operator complexities,” [arXiv:2212.10583 [hep-th]]

Original

Cited in the paper.

M. R. Douglas, I. R. Klebanov, D. Kutasov, J. M. Maldacena, E. J. Martinec and N. Seiberg, “A New hat for the c=1 matrix model,” [arXiv:hep-th/0307195 [hep-th]]

Cited in the paper.

M. Alishahiha and S. Banerjee, “On the saturation of late-time growth of complexity in supersymmetric JT gravity,” [arXiv:2209.02441 [hep-th]]

Original

Cited in the paper.

, R. Szmytkowski and S. Bielski, “An orthogonality relation for the Whittaker functions of the second kind of imaginary order,” arXiv:0910.1492 [math.CA]

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Cited in the paper.

Original

2022

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V. Balasubramanian, P. Caputa, J. M. Magan and Q. Wu, “Quantum chaos and the complexity of spread of states,” Phys. Rev. D 106

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2022

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J. M. Deutsch, “Quantum statistical mechanics in a closed system,” Phys Rev A. 43

2046

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