Abstract
The strength of chaos in large N quantum systems can be quantified using λ L , the rate of growth of certain out-of-time-order four point functions. We calculate λ L to leading order in a weakly coupled matrix Φ4 theory by numerically diagonalizing a ladder kernel. The computation reduces to an essentially classical problem.
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References
A.I. Larkin and Y.N. Ovchinnikov, Quasiclassical method in the theory of superconductivity, JETP 28 (1969) 1200.
A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, An Apologia for Firewalls, JHEP 09 (2013) 018 [arXiv:1304.6483] [INSPIRE].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
S.H. Shenker and D. Stanford, Multiple Shocks, JHEP 12 (2014) 046 [arXiv:1312.3296] [INSPIRE].
D.A. Roberts, D. Stanford and L. Susskind, Localized shocks, JHEP 03 (2015) 051 [arXiv:1409.8180] [INSPIRE].
A. Kitaev, Hidden Correlations in the Hawking Radiation and Thermal Noise, talk given at Fundamental Physics Prize Symposium, 10 November 2014.
A. Kitaev, Hidden Correlations in the Hawking Radiation and Thermal Noise, Stanford SITP seminars, November 11 and December 18 2014.
S.H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 05 (2015) 132 [arXiv:1412.6087] [INSPIRE].
D.A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect, Phys. Rev. Lett. 115 (2015) 131603 [arXiv:1412.5123] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
E.A. Kuraev, L.N. Lipatov and V.S. Fadin, The Pomeranchuk Singularity in Nonabelian Gauge Theories, Sov. Phys. JETP 45 (1977) 199 [Zh. Eksp. Teor. Fiz. 72 (1977) 377] [INSPIRE].
I.I. Balitsky and L.N. Lipatov, The Pomeranchuk Singularity in Quantum Chromodynamics, Sov. J. Nucl. Phys. 28 (1978) 822 [INSPIRE].
S. Jeon, Hydrodynamic transport coefficients in relativistic scalar field theory, Phys. Rev. D 52 (1995) 3591 [hep-ph/9409250] [INSPIRE].
J.R. Forshaw and D.A. Ross, Quantum chromodynamics and the pomeron, Cambridge Lect. Notes Phys. 9 (1997) 1.
A. Kitaev, A simple model of quantum holography, talks given at KITP program “Entanglement in Strongly-Correlated Quantum Matter”, April 7 and May 27 2015.
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
O. Parcollet and A. Georges, Non-Fermi-liquid regime of a doped Mott insulator, Phys. Rev. B 59 (1999) 5341.
S. Sachdev, Bekenstein-Hawking Entropy and Strange Metals, Phys. Rev. X 5 (2015) 041025 [arXiv:1506.05111] [INSPIRE].
R.R. Parwani, Resummation in a hot scalar field theory, Phys. Rev. D 45 (1992) 4695 [Erratum ibid. D 48 (1993) 5965] [hep-ph/9204216] [INSPIRE].
Y. Sekino and L. Susskind, Fast Scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].
R. Omnès, On locality, growth and transport of entanglement, arXiv:1212.0331.
H. Kim and D.A. Huse, Ballistic spreading of entanglement in a diffusive nonintegrable system, Phys. Rev. Lett. 111 (2013) 127205 [arXiv:1306.4306].
G. Gur-Ari, M. Hanada and S.H. Shenker, Chaos in Classical D0-Brane Mechanics, JHEP 02 (2016) 091 [arXiv:1512.00019] [INSPIRE].
A.H. Mueller and D.T. Son, On the Equivalence between the Boltzmann equation and classical field theory at large occupation numbers, Phys. Lett. B 582 (2004) 279 [hep-ph/0212198] [INSPIRE].
S. Jeon, The Boltzmann equation in classical and quantum field theory, Phys. Rev. C 72 (2005) 014907 [hep-ph/0412121] [INSPIRE].
V. Mathieu, A.H. Mueller and D.N. Triantafyllopoulos, The Boltzmann Equation in Classical Yang-Mills Theory, Eur. Phys. J. C 74 (2014) 2873 [arXiv:1403.1184] [INSPIRE].
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ArXiv ePrint: 1512.07687
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Stanford, D. Many-body chaos at weak coupling. J. High Energ. Phys. 2016, 9 (2016). https://doi.org/10.1007/JHEP10(2016)009
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DOI: https://doi.org/10.1007/JHEP10(2016)009