Abstract
We study the effect of a non-vanishing chemical potential on the thermalization time of a strongly coupled large N c gauge theory in (2 + 1)-dimensions, using a specific bottom-up gravity model in asymptotically AdS space. We first construct a perturbative solution to the gravity-equations, which dynamically interpolates between two AdS black hole backgrounds with different temperatures and chemical potentials, in a perturbative expansion of a bulk neutral scalar field. In the dual field theory, this corresponds to a quench dynamics by a marginal operator, where the corresponding coupling serves as the small parameter in which the perturbation is carried out. The evolution of non-local observables, such as the entanglement entropy, suggests that thermalization time decreases with increasing chemical potential. We also comment on the validity of our perturbative analysis.
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J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, arXiv:1101.0618 [INSPIRE].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
S. Mondal, D. Sen and K. Sengupta, Non-equilibrium dynamics of quantum systems: order parameter evolution, defect generation, and qubit transfer, Lect. Notes. Phys. 802 (2010) 21 [arXiv:0908.2922].
J. Dziarmaga, Dynamics of a quantum phase transition and relaxation to a steady state, Adv. Phys. 59 (2010) 1063 [arXiv:0912.4034].
A. Polkovnikov, K. Sengupta, A. Silva and M. Vengalattore, Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83 (2011) 863 [arXiv:1007.5331] [INSPIRE].
S.R. Das, Holographic Quantum Quench, J. Phys. Conf. Ser. 343 (2012) 012027 [arXiv:1111.7275] [INSPIRE].
P. Basu and S.R. Das, Quantum Quench across a Holographic Critical Point, JHEP 01 (2012) 103 [arXiv:1109.3909] [INSPIRE].
S.R. Das, T. Nishioka and T. Takayanagi, Probe Branes, Time-dependent Couplings and Thermalization in AdS/CFT, JHEP 07 (2010) 071 [arXiv:1005.3348] [INSPIRE].
U.H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, Spherically collapsing matter in AdS, holography and shellons, Nucl. Phys. B 563 (1999) 279 [hep-th/9905227] [INSPIRE].
U.H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, Black hole formation in AdS and thermalization on the boundary, JHEP 02 (2000) 039 [hep-th/9912209] [INSPIRE].
S.B. Giddings and A. Nudelman, Gravitational collapse and its boundary description in AdS, JHEP 02 (2002) 003 [hep-th/0112099] [INSPIRE].
P.M. Chesler and L.G. Yaffe, Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 102 (2009) 211601 [arXiv:0812.2053] [INSPIRE].
P.M. Chesler and L.G. Yaffe, Boost invariant flow, black hole formation and far-from-equilibrium dynamics in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. D 82 (2010) 026006 [arXiv:0906.4426] [INSPIRE].
M.P. Heller, R.A. Janik and P. Witaszczyk, The characteristics of thermalization of boost-invariant plasma from holography, Phys. Rev. Lett. 108 (2012) 201602 [arXiv:1103.3452] [INSPIRE].
M.P. Heller, R.A. Janik and P. Witaszczyk, A numerical relativity approach to the initial value problem in asymptotically Anti-de Sitter spacetime for plasma thermalization — an ADM formulation, Phys. Rev. D 85 (2012) 126002 [arXiv:1203.0755] [INSPIRE].
M.P. Heller, D. Mateos, W. van der Schee and D. Trancanelli, Strong Coupling Isotropization of Non-Abelian Plasmas Simplified, Phys. Rev. Lett. 108 (2012) 191601 [arXiv:1202.0981] [INSPIRE].
J. Casalderrey-Solana, M.P. Heller, D. Mateos and W. van der Schee, From full stopping to transparency in a holographic model of heavy ion collisions, Phys. Rev. Lett. 111 (2013) 181601 [arXiv:1305.4919] [INSPIRE].
W. van der Schee, P. Romatschke and S. Pratt, Fully Dynamical Simulation of Central Nuclear Collisions, Phys. Rev. Lett. 111 (2013) 222302 [arXiv:1307.2539] [INSPIRE].
J. Casalderrey-Solana, M.P. Heller, D. Mateos and W. van der Schee, Longitudinal Coherence in a Holographic Model of Asymmetric Collisions, Phys. Rev. Lett. 112 (2014) 221602 [arXiv:1312.2956] [INSPIRE].
V. Balasubramanian et al., Inhomogeneous Thermalization in Strongly Coupled Field Theories, Phys. Rev. Lett. 111 (2013) 231602 [arXiv:1307.1487] [INSPIRE].
V. Balasubramanian et al., Inhomogeneous holographic thermalization, JHEP 10 (2013) 082 [arXiv:1307.7086] [INSPIRE].
B. Craps, E. Kiritsis, C. Rosen, A. Taliotis, J. Vanhoof and H. Zhang, Gravitational collapse and thermalization in the hard wall model, JHEP 02 (2014) 120 [arXiv:1311.7560] [INSPIRE].
V. Cardoso, R. Emparan, D. Mateos, P. Pani and J.V. Rocha, Holographic collisions in confining theories, JHEP 01 (2014) 138 [arXiv:1310.7590] [INSPIRE].
D. Fernández, Towards Collisions of Inhomogeneous Shockwaves in AdS, arXiv:1407.5628 [INSPIRE].
S. Bhattacharyya and S. Minwalla, Weak Field Black Hole Formation in Asymptotically AdS Spacetimes, JHEP 09 (2009) 034 [arXiv:0904.0464] [INSPIRE].
D. Garfinkle, L.A. Pando Zayas and D. Reichmann, On Field Theory Thermalization from Gravitational Collapse, JHEP 02 (2012) 119 [arXiv:1110.5823] [INSPIRE].
P. Bizon and A. Rostworowski, On weakly turbulent instability of anti-de Sitter space, Phys. Rev. Lett. 107 (2011) 031102 [arXiv:1104.3702] [INSPIRE].
V. Balasubramanian, A. Buchel, S.R. Green, L. Lehner and S.L. Liebling, Holographic Thermalization, Stability of Anti de Sitter Space and the Fermi-Pasta-Ulam Paradox, Phys. Rev. Lett. 113 (2014) 071601 [arXiv:1403.6471] [INSPIRE].
A. Buchel, S.R. Green, L. Lehner and S.L. Liebling, Universality of non-equilibrium dynamics of CFTs from holography, arXiv:1410.5381 [INSPIRE].
J. Abajo-Arrastia, E. da Silva, E. Lopez, J. Mas and A. Serantes, Holographic Relaxation of Finite Size Isolated Quantum Systems, JHEP 05 (2014) 126 [arXiv:1403.2632] [INSPIRE].
J. Abajo-Arrastia, J. Aparicio and E. Lopez, Holographic Evolution of Entanglement Entropy, JHEP 11 (2010) 149 [arXiv:1006.4090] [INSPIRE].
V. Balasubramanian et al., Thermalization of Strongly Coupled Field Theories, Phys. Rev. Lett. 106 (2011) 191601 [arXiv:1012.4753] [INSPIRE].
V. Balasubramanian et al., Holographic Thermalization, Phys. Rev. D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].
T. Albash and C.V. Johnson, Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches, New J. Phys. 13 (2011) 045017 [arXiv:1008.3027] [INSPIRE].
D. Galante and M. Schvellinger, Thermalization with a chemical potential from AdS spaces, JHEP 07 (2012) 096 [arXiv:1205.1548] [INSPIRE].
E. Caceres and A. Kundu, Holographic Thermalization with Chemical Potential, JHEP 09 (2012) 055 [arXiv:1205.2354] [INSPIRE].
E. Caceres, A. Kundu and D.-L. Yang, Jet Quenching and Holographic Thermalization with a Chemical Potential, JHEP 03 (2014) 073 [arXiv:1212.5728] [INSPIRE].
A. Andronic, P. Braun-Munzinger and J. Stachel, Hadron production in central nucleus-nucleus collisions at chemical freeze-out, Nucl. Phys. A 772 (2006) 167 [nucl-th/0511071] [INSPIRE].
J. Stachel, A. Andronic, P. Braun-Munzinger and K. Redlich, Confronting LHC data with the statistical hadronization model, J. Phys. Conf. Ser. 509 (2014) 012019 [arXiv:1311.4662] [INSPIRE].
A. Buchel, L. Lehner and R.C. Myers, Thermal quenches in N = 2∗ plasmas, JHEP 08 (2012) 049 [arXiv:1206.6785] [INSPIRE].
A. Buchel, L. Lehner, R.C. Myers and A. van Niekerk, Quantum quenches of holographic plasmas, JHEP 05 (2013) 067 [arXiv:1302.2924] [INSPIRE].
A. Buchel, R.C. Myers and A. van Niekerk, Nonlocal probes of thermalization in holographic quenches with spectral methods, JHEP 02 (2015) 017 [arXiv:1410.6201] [INSPIRE].
E. Caceres, A. Kundu, J.F. Pedraza and W. Tangarife, Strong Subadditivity, Null Energy Condition and Charged Black Holes, JHEP 01 (2014) 084 [arXiv:1304.3398] [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
K. Skenderis, Asymptotically Anti-de Sitter space-times and their stress energy tensor, Int. J. Mod. Phys. A 16 (2001) 740 [hep-th/0010138] [INSPIRE].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].
A. Buchel, R.C. Myers and A. van Niekerk, Universality of Abrupt Holographic Quenches, Phys. Rev. Lett. 111 (2013) 201602 [arXiv:1307.4740] [INSPIRE].
S.R. Das, D.A. Galante and R.C. Myers, Universal scaling in fast quantum quenches in conformal field theories, Phys. Rev. Lett. 112 (2014) 171601 [arXiv:1401.0560] [INSPIRE].
S.R. Das, D.A. Galante and R.C. Myers, Universality in fast quantum quenches, JHEP 02 (2015) 167 [arXiv:1411.7710] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
M. Nozaki, T. Numasawa and T. Takayanagi, Holographic Local Quenches and Entanglement Density, JHEP 05 (2013) 080 [arXiv:1302.5703] [INSPIRE].
J.F. Pedraza, Evolution of nonlocal observables in an expanding boost-invariant plasma, Phys. Rev. D 90 (2014) 046010 [arXiv:1405.1724] [INSPIRE].
H. Liu and S.J. Suh, Entanglement Tsunami: Universal Scaling in Holographic Thermalization, Phys. Rev. Lett. 112 (2014) 011601 [arXiv:1305.7244] [INSPIRE].
H. Liu and S.J. Suh, Entanglement growth during thermalization in holographic systems, Phys. Rev. D 89 (2014) 066012 [arXiv:1311.1200] [INSPIRE].
M. Alishahiha, A.F. Astaneh and M.R.M. Mozaffar, Thermalization in backgrounds with hyperscaling violating factor, Phys. Rev. D 90 (2014) 046004 [arXiv:1401.2807] [INSPIRE].
P. Fonda, L. Franti, V. Keränen, E. Keski-Vakkuri, L. Thorlacius and E. Tonni, Holographic thermalization with Lifshitz scaling and hyperscaling violation, JHEP 08 (2014) 051 [arXiv:1401.6088] [INSPIRE].
M. Alishahiha, M.R.M. Mozaffar and M.R. Tanhayi, Evolution of Holographic n-partite Information, arXiv:1406.7677 [INSPIRE].
W. Fischler, S. Kundu and J.F. Pedraza, Entanglement and out-of-equilibrium dynamics in holographic models of de Sitter QFTs, JHEP 07 (2014) 021 [arXiv:1311.5519] [INSPIRE].
Y. Sekino and L. Susskind, Fast Scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].
L. Susskind, Addendum to Fast Scramblers, arXiv:1101.6048 [INSPIRE].
N. Lashkari, D. Stanford, M. Hastings, T. Osborne and P. Hayden, Towards the Fast Scrambling Conjecture, JHEP 04 (2013) 022 [arXiv:1111.6580] [INSPIRE].
M. Edalati, W. Fischler, J.F. Pedraza and W. Tangarife Garcia, Fast Scramblers and Non-commutative Gauge Theories, JHEP 07 (2012) 043 [arXiv:1204.5748] [INSPIRE].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
S. Leichenauer, Disrupting Entanglement of Black Holes, Phys. Rev. D 90 (2014) 046009 [arXiv:1405.7365] [INSPIRE].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [INSPIRE].
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Caceres, E., Kundu, A., Pedraza, J.F. et al. Weak field collapse in AdS: introducing a charge density. J. High Energ. Phys. 2015, 111 (2015). https://doi.org/10.1007/JHEP06(2015)111
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DOI: https://doi.org/10.1007/JHEP06(2015)111