Built on

A. W. Harrow and R. A. Low, “Random quantum circuits are approximate 2-designs,” Comm.Math.Phys. 291
Original
1919
Earlier work this paper cites.
A. I. Larkin and Y. N. Ovchinnikov, “Quasiclassical method in the theory of superconductivity,” JETP 28, 6 (1969): 1200-1205
1969
Earlier work this paper cites.
E. H. Lieb and D. W. Robinson, “The finite group velocity of quantum spin systems,” Commun. Math. Phys. 28
1972
Earlier work this paper cites.
T. Dray and G. ’t Hooft, “The Gravitational Shock Wave of a Massless Particle,” Nucl. Phys. B 253
1985
Earlier work this paper cites.
G. ’t Hooft, “The black hole interpretation of string theory,” Nucl. Phys. B 335
1990
Earlier work this paper cites.
Y. Kiem, H. L. Verlinde and E. P. Verlinde, “Black hole horizons and complementarity,” Phys. Rev. D 52
1995
Earlier work this paper cites.
K. Sfetsos, “On gravitational shock waves in curved space-times,” Nucl. Phys. B 436
1995
Earlier work this paper cites.
P. Kovtun, D. T. Son and A. O. Starinets, “Viscosity in strongly interacting quantum field theories from black hole physics,” Phys. Rev. Lett. 94
2005
Earlier work this paper cites.
M. B. Hastings and T. Koma, “Spectral gap and exponential decay of correlations,” Commun. Math. Phys. 265
2006
Earlier work this paper cites.

Similar

P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” JHEP 0709
Original
2007
Cited alongside, same era.
R. C. Brower, J. Polchinski, M. J. Strassler and C. -ITan, “The Pomeron and gauge/string duality,” JHEP 0712
2007
Cited alongside, same era.
L. Cornalba, M. S. Costa, J. Penedones and R. Schiappa, “Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions,” JHEP 0708
2007
Cited alongside, same era.
L. Arnaud and D. Braun, “Efficiency of producing random unitary matrices with quantum circuits,” Phys.Rev. A78
Original
2008
Cited alongside, same era.
M. Brigante, H. Liu, R. C. Myers, S. Shenker and S. Yaida, “Viscosity Bound Violation in Higher Derivative Gravity,” Phys. Rev. D 77
Original

Then

W. G. Brown and L. Viola, “Convergence rates for arbitrary statistical moments of random quantum circuits,” Phys.Rev.Lett. 104
Original
2010
Later among the works it cites.
T. Banks and G. Festuccia, “The Regge Limit for Green Functions in Conformal Field Theory,” JHEP 1006
Original
2010
Later among the works it cites.
I. T. Diniz and D. Jonathan, “Comment on the paper ‘Random quantum circuits are approximate 2-designs’,” Comm.Math.Phys. 304
Original
2011
Later among the works it cites.
A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, “An Apologia for Firewalls,” JHEP 1309
Original
2013
Later among the works it cites.
N. Lashkari, D. Stanford, M. Hastings, T. Osborne and P. Hayden, “Towards the Fast Scrambling Conjecture,” JHEP 1304

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2015

A bound on chaos

Maldacena, Juan, Shenker, Stephen H., Stanford, Douglas

Understand

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom.

Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time.
We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent $\lambda_L \le 2 \pi k_B T/\hbar$.
We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

Built on

A. W. Harrow and R. A. Low, “Random quantum circuits are approximate 2-designs,” Comm.Math.Phys. 291
Original
1919
Earlier work this paper cites.
A. I. Larkin and Y. N. Ovchinnikov, “Quasiclassical method in the theory of superconductivity,” JETP 28, 6 (1969): 1200-1205
1969
Earlier work this paper cites.
E. H. Lieb and D. W. Robinson, “The finite group velocity of quantum spin systems,” Commun. Math. Phys. 28
1972
Earlier work this paper cites.
T. Dray and G. ’t Hooft, “The Gravitational Shock Wave of a Massless Particle,” Nucl. Phys. B 253
1985
Earlier work this paper cites.
G. ’t Hooft, “The black hole interpretation of string theory,” Nucl. Phys. B 335
1990
Earlier work this paper cites.
Y. Kiem, H. L. Verlinde and E. P. Verlinde, “Black hole horizons and complementarity,” Phys. Rev. D 52
1995
Earlier work this paper cites.
K. Sfetsos, “On gravitational shock waves in curved space-times,” Nucl. Phys. B 436
1995
Earlier work this paper cites.
P. Kovtun, D. T. Son and A. O. Starinets, “Viscosity in strongly interacting quantum field theories from black hole physics,” Phys. Rev. Lett. 94
2005
Earlier work this paper cites.
M. B. Hastings and T. Koma, “Spectral gap and exponential decay of correlations,” Commun. Math. Phys. 265
2006
Earlier work this paper cites.

Similar

P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” JHEP 0709
Original
2007
Cited alongside, same era.
R. C. Brower, J. Polchinski, M. J. Strassler and C. -ITan, “The Pomeron and gauge/string duality,” JHEP 0712
2007
Cited alongside, same era.
L. Cornalba, M. S. Costa, J. Penedones and R. Schiappa, “Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions,” JHEP 0708
2007
Cited alongside, same era.
L. Arnaud and D. Braun, “Efficiency of producing random unitary matrices with quantum circuits,” Phys.Rev. A78
Original
2008
Cited alongside, same era.
M. Brigante, H. Liu, R. C. Myers, S. Shenker and S. Yaida, “Viscosity Bound Violation in Higher Derivative Gravity,” Phys. Rev. D 77
Original

Then

W. G. Brown and L. Viola, “Convergence rates for arbitrary statistical moments of random quantum circuits,” Phys.Rev.Lett. 104
Original
2010
Later among the works it cites.
T. Banks and G. Festuccia, “The Regge Limit for Green Functions in Conformal Field Theory,” JHEP 1006
Original
2010
Later among the works it cites.
I. T. Diniz and D. Jonathan, “Comment on the paper ‘Random quantum circuits are approximate 2-designs’,” Comm.Math.Phys. 304
Original
2011
Later among the works it cites.
A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, “An Apologia for Firewalls,” JHEP 1309
Original
2013
Later among the works it cites.
N. Lashkari, D. Stanford, M. Hastings, T. Osborne and P. Hayden, “Towards the Fast Scrambling Conjecture,” JHEP 1304

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

2008

Cited alongside, same era.

M. Brigante, H. Liu, R. C. Myers, S. Shenker and S. Yaida, “The Viscosity Bound and Causality Violation,” Phys. Rev. Lett. 100

Original

2008

Cited alongside, same era.

C. Dankert, R. Cleve, J. Emerson, and E. Livine, “Exact and approximate unitary 2-designs and their application to fidelity estimation,” Phys.Rev. A80

2009

Cited alongside, same era.

Y. Kats and P. Petrov, “Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory,” JHEP 0901

Original

2009

Cited alongside, same era.

I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, “Holography from Conformal Field Theory,” JHEP 0910

Original

2009

Cited alongside, same era.

D. A. Roberts, D. Stanford and L. Susskind, “Localized shocks,” arXiv:1409.8180 [hep-th]

Original

Cited in the paper.

M. B. Hastings, “Locality in quantum systems,” arXiv:1008.5137 [math-ph]

Original

Cited in the paper.

W. Brown and O. Fawzi, “Scrambling speed of random quantum circuits,” arXiv:1210.6644 [quant-ph]

Original

Cited in the paper.

Original

2013

Later among the works it cites.

S. H. Shenker and D. Stanford, “Black holes and the butterfly effect,” JHEP 1403

Original

2014

Later among the works it cites.

S. H. Shenker and D. Stanford, “Multiple Shocks,” JHEP 1412

Original

2014

Later among the works it cites.

A. Kitaev, “Hidden Correlations in the Hawking Radiation and Thermal Noise,” talk given at Fundamental Physics Prize Symposium, Nov. 10, 2014. Stanford SITP seminars, Nov. 11 and Dec. 18, 2014

2014

Later among the works it cites.

Y. Sekino and L. Susskind, “Fast Scramblers,” JHEP 0810

Original

2096

Closest in time.