AdS黑洞中量子复杂度的晚期增长率与自由能关系

doi:10.12066/j.issn.1007-2861.2314

摘要/Abstract

摘要：

量子复杂度与自由能的关系研究为复杂度-作用量猜想和复杂度-体积猜想之间搭起了一座桥梁. 首先, 通过无奇点的Bardeen-AdS黑洞、 $f(R)$引力下的带电黑洞和Born-Infeld AdS黑洞检验量子复杂度晚期增长率与自由能关系的普适性; 然后, 讨论了将量子复杂度晚期增长率作为探针研究相变的可能性; 最后, 研究了量子复杂度晚期增长率是否违反Lloyd上限的问题.

关键词: 量子复杂度, 黑洞热力学, AdS黑洞

Abstract:

The relationship between quantum complexity and free energy relation builds a bridge between the complexity action duality and complexity volume duality. The main purpose of this study is to investigate the universality of the quantum complexity and free energy relation by verifying in Bardeen-AdS black holes without singularities, charged black holes in $f(R)$ modified gravity, and Born-Infeld AdS black holes. The possibility of using quantum complexity as a probe in analysing phase transitions is evaluated. Finally, whether the late-time quantum complexity rates violated the Lloyd bound is verified.

Key words: quantum complexity, black hole thermodynamics, AdS black holes

中图分类号:

O412

孙威, 葛先辉. AdS黑洞中量子复杂度的晚期增长率与自由能关系[J]. 上海大学学报(自然科学版), 2022, 28(6): 1069-1083.

SUN Wei, GE Xianhui. Relationship between late-time quantum complexity growth rate and free energy in AdS black holes[J]. Journal of Shanghai University（Natural Science Edition）, 2022, 28(6): 1069-1083.

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参考文献 57

[1]	Maldacena J M. The large $N$ limit of superconformal field theories and supergravity[EB/OL]. [2021-12-09]. https://www.doc88.com/p-6129771812350.html.
[2]	Gubser S S, Klebanov I R, Polyakov A M. Gauge theory correlators from non-critical string theory[J]. Physics Letters B, 1998, 428(1/2): 105-114.
[3]	Witten E. Anti de sitter space and holography[EB/OL]. [2021-12-30]. https://www.docin.com/p-1443927043.html.
[4]	Aharony O, Gubser S S, Maldacena J M, et al. Large $N$ field theories, string theory and gravity[J]. Physics Reports, 1999, 323(3/4): 183-386.
[5]	Ryu S, Takayanagi T. Holographic derivation of entanglement entropy from AdS/CFT[EB/OL]. [2020-11-03]. https://xueshu.baidu.com/usercenter/paper/show?paperid=b9cb41665adf868454ffedfc065b3b97.
[6]	Maldacena J. Eternal black holes in anti-de sitter[J]. Journal of High Energy Physics, 2003(4): 021.
[7]	Hartman T, Maldacena J. Time evolution of entanglement entropy from black holeinteriors[J]. Journal of High Energy Physics, 2013, 2013(5): 014.
[8]	Susskind L. Butterflies on the stretched horizon[EB/OL]. [2021-01-02]. https://xueshu.baidu.com/usercenter/paper/show?paperid=fba455c20997f9ad91c519bf0047233a.
[9]	Susskind L. Computational complexity and black hole horizons[J]. Fortschritte der Physik, 2016, 64(1): 24-43.
[10]	Susskind L. Addendum to computational complexity and black hole horizons[J]. Fortschritte der Physik, 2016, 64(1): 44-48.
[11]	Stanford D, Susskind L. Complexity and shock wave geometries[J]. Physical Review D, 2014, 90(12): 126007.
[12]	Brown A R, Roberts D A, Susskind L, et al. Holographic complexity equals bulkaction?[J]. Physical Review Letters, 2016, 116(19): 191301.
[13]	Sun W, Ge X H. Complexity growth rate, grand potential and partition function[EB/OL]. [2020-10-08]. https://xueshu.baidu.com/usercenter/paper/show?paperid=1v330pm0nx0v0rw0470e0c70t6674185&site=xueshu_se.
[14]	Hayden P, Preskill J. Black holes as mirrors: quantum information in randomsubsystems[J]. Journal of High Energy Physics, 2007, 2007(9): 887-891.
[15]	Kastor D, Ray S, Traschen J. Enthalpy and the mechanics of AdS black holes[J]. Classical & Quantum Gravity, 2009, 26(19): 2551-2563.
[16]	Kubiznak D, Mann R B. Black hole chemistry[J]. Canadian Journal of Physics, 2014, 93(9): 999-1002.
[17]	Dolan B P. Where is the PdV term in the first law of black hole thermodynamics?[J]. Physics, 2012, 28(23): 235017-235029.
[18]	Frassino A M, Mann R B, Mureika J R. Lower-dimensional black hole chemistry[J]. Physical Review D, 2015, 92(12): 124069.
[19]	Kubiznak D, Mann R B, Teo M. Black hole chemistry: thermodynamics with lambda[J]. Classical and Quantum Gravity, 2016, 34(6): 063001.
[20]	Johnson C V. Holographic heat engines[J]. Classical & Quantum Gravity, 2014, 31(20): 205002.
[21]	Couch J, Fischler W, Nguyen P H. Noether charge, black hole volume, and complexity[EB/OL]. [2020-12-01]. https://www.doc88.com/p-7488992990174.html?r=1.
[22]	Pathria R K. Statistical mechanics[M]. 2nd ed. Amsterdam: Elsevier, 1996.
[23]	Bardeen J M. Non-singular general-relativistic gravitational collapse[EB/OL]. [2021-11-02]. https://xueshu.baidu.com/usercenter/paper/show?paperid=bb94773011c28c35f45462ed21db84ed.
[24]	Ayón-Beato E, García A. The Bardeen model as a nonlinear magnetic monopole[J]. Physics Letters B, 2000, 493(1): 149-152.
[25]	Li C, Fang C, He M, et al. Thermodynamics of the bardeen black hole in anti-de sitter space[EB/OL]. [2021-10-01]. http://www.doc88.com/p-7304822319658.html.
[26]	Hawking S W, Page D N. Thermodynamics of black holes in anti-de Sitter space[J]. Communications in Mathematical Physics, 1983, 87(4): 577-588.
[27]	Banerjee R, Roychowdhury D. Critical behavior of Born infeld AdS black holes in higher dimensions[J]. Physical Review D: Particles and Fields, 2012(85): 96-106.
[28]	Cai R G, Pang D W, Wang A. Born-Infeld black holes in (A)dS spaces[J]. Physical Review D, 2004, 70(12): 317-324.
[29]	Dey T K. Born-Infeld black holes in the presence of a cosmological constant[J]. Physics Letters B, 2004, 595(1/2/3/4): 484-490.
[30]	Zou D C, ZJANG S J, Wang B. Critical behavior of Born-Infeld AdS black holes in the extended phase space thermodynamics[EB/OL]. [2021-05-06]. https://arxiv.org/abs/1311.7299v2.
[31]	Gunasekaran S, Kubizňák D, Mann R B. Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization[J]. Journal of High Energy Physics, 2012, 2012(11): 110.
[32]	Moon T, Myung Y S, Son E J. $f (R)$ black holes[J]. General Relativity & Gravitation, 2011, 43: 3079-3098.
[33]	Sheykhi A. Higher dimensional charged $f (R)$ black holes[J]. Physical Review D, 2012, 86(2): 024013.
[34]	Jordan S P. Fast quantum computation at arbitrarily low energy[J]. Physical Review A, 2017, 95(3): 032305.
[35]	Sinitsyn N A. Computing with a single qubit faster than the computation quantum speedlimit[J]. Physics Letters A, 2017, 382(7): 477-481.
[36]	Lloyd S, Ng Y J. Black hole computers[J]. Scientific American, 2004, 291(5): 30-39.
[37]	Levitin M. The maximum speed of dynamical evolution[J]. Physica D: Nonlinear Phenomena, 1998, 120: 188-195.
[38]	Brown A R, Roberts D A, Susskind L, et al. Complexity, action, and black holes[J]. Physical Review D, 2015, 8: 086006.
[39]	Tao J, Wang P, Yang H. Testing holographic conjectures of complexity with Born-Infeld black holes[J]. European Physical Journal C, 2017, 77(12): 817.
[40]	Peng W, Yang H, Ying S. Action growth in $f(R)$ gravity[J]. Physical Review D, 2017, 96(4): 046007.
[41]	Zhang S J. Complexity and phase transitions in a holographic QCD model[J]. Nuclear Physics B, 2018, 929: 243-253.
[42]	Gubser S S, Nellore A. Mimicking the QCD equation of state with a dual black hole[J]. Physical Review D, 2008, 78(8): 086007.
[43]	Gubser S S, Nellore A, Pufu S S, et al. Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics[J]. Physical Review Letters, 2008, 101(13): 6216-6220.
[44]	Gürsoy U, Kiritsis E, Nitti F. Exploring improved holographic theories for QCD: part Ⅱ[J]. Journal of High Energy Physics, 2008, 2008(2): 019.
[45]	Gürsoy U, Kiritsis E, Mazzanti L, et al. Holography and thermodynamics of 5D dilaton-gravity[J]. Journal of High Energy Physics, 2009, 2009(5): 033.
[46]	Kiritsis E. Dissecting the string theory dual of QCD[J]. Fortschritte Der Physik, 2009, 57(5/6/7): 396-417.
[47]	Gürsoy U, Kiritsis E, Mazzanti L, et al. Improved holographic Yang-Mills at finite temperature: comparison with data[J]. Nuclear Physics B, 2009, 820(1/2): 148-177.
[48]	Buchel A, Deakin S, Kerner P, et al. Thermodynamics of the strongly coupled plasma[J]. Nuclear Physics B, 2007, 784: 72-102.
[49]	Buchel A, Heller M P, Myers R C. Equilibration rates in a strongly coupled nonconformal quark-gluon plasma[J]. Physical Review Letters, 2015, 114(25): 251601.
[50]	Li D N, He S, Huang M, et al. Thermodynamics of deformed AdS5 model with a positive/negative quadratic correction in graviton-dilaton system[EB/OL]. [2020-12-06]. https://xueshu.baidu.com/usercenter/paper/show?paperid=516817a8d4f187721d9ea4049b321e36.
[51]	Cai R G, He S, Li D. A hQCD model and its phase diagram in Einstein-Maxwell-Dilaton system[J]. Journal of High Energy Physics, 2012, 2012(3): 033.
[52]	Hartnoll S A. Lectures on holographic methods for condensed matter physics[J]. Classical & Quantum Gravity, 2009, 26(22): 1913-1941.
[53]	Herzog C P. Lectures on holographic superfluidity and superconductivity[J]. Journal of Physics A Mathematical & Theoretical, 2009, 42(34): 343001.
[54]	Mcgreevy J. Holographic duality with a view toward many-body physics[J]. Advances in High Energy Physics, 2009, 2010(3/4): 723105.
[55]	Horowitz G T. Introduction to holographic superconductors[J]. Lecture Notes in Physics, 2010, 828: 313-347.
[56]	Cai R G, Li L, Li L F, et al. Introduction to holographic superconductor models[J]. Science China: Physics, Mechanics & Astronomy, 2015, 58(6): 1-46.
[57]	Ge X H, Wang B. Quantum computational complexity, Einstein's equations and accelerated expansion of the Universe[J]. Journal of Cosmology & Astroparticle Physics, 2018(2): 47.