Abstract
Correlation functions of most composite operators decay exponentially with time at non-zero temperature, even in free field theories. This insight was recently codified in an OTH (operator thermalisation hypothesis). We reconsider an early example, with large N free fields subjected to a singlet constraint. This study in dimensions d > 2 motivates technical modifications of the original OTH to allow for generalised free fields. Furthermore, Huygens’ principle, valid for wave equations only in even dimensions, leads to differences in thermalisation. It works straightforwardly when Huygens’ principle applies, but thermalisation is more elusive if it does not apply. Instead, in odd dimensions we find a link to resurgence theory by noting that exponential relaxation is analogous to non- perturbative corrections to an asymptotic perturbation expansion. Without applying the power of resurgence technology we still find support for thermalisation in odd dimensions, although these arguments are incomplete.
Article PDF
Similar content being viewed by others
References
J.M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43 (1991) 2046.
M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50 (1994) 888.
P. Calabrese and J.L. Cardy, Time-dependence of correlation functions following a quantum quench, Phys. Rev. Lett. 96 (2006) 136801 [cond-mat/0601225] [INSPIRE].
P. Calabrese and J. Cardy, Quantum Quenches in Extended Systems, J. Stat. Mech. 0706 (2007) P06008 [arXiv:0704.1880] [INSPIRE].
S.R. Das, D.A. Galante and R.C. Myers, Quantum Quenches in Free Field Theory: Universal Scaling at Any Rate, JHEP 05 (2016) 164 [arXiv:1602.08547] [INSPIRE].
S. Banerjee, J. Engelsöy, J. Larana-Aragon, B. Sundborg, L. Thorlacius and N. Wintergerst, Quenched coupling, entangled equilibria, and correlated composite operators: a tale of two O(N) models, JHEP 08 (2019) 139 [arXiv:1903.12242] [INSPIRE].
M. Rigol, V. Dunjko, V. Yurovsky and M. Olshanii, Relaxation in a completely integrable many-body quantum system: An ab initio study of the dynamics of the highly excited states of 1d lattice hard-core bosons, Phys. Rev. Lett. 98 (2007) 050405.
J. Cardy, Quantum Quenches to a Critical Point in One Dimension: some further results, J. Stat. Mech. 1602 (2016) 023103 [arXiv:1507.07266] [INSPIRE].
A. Dymarsky and K. Pavlenko, Generalized Eigenstate Thermalization Hypothesis in 2D Conformal Field Theories, Phys. Rev. Lett. 123 (2019) 111602 [arXiv:1903.03559] [INSPIRE].
I. Amado, B. Sundborg, L. Thorlacius and N. Wintergerst, Black holes from large N singlet models, JHEP 03 (2018) 075 [arXiv:1712.06963] [INSPIRE].
S. Banerjee, K. Papadodimas, S. Raju, P. Samantray and P. Shrivastava, A Bound on Thermal Relativistic Correlators at Large Spacelike Momenta, SciPost Phys. 8 (2020) 064 [arXiv:1902.07203] [INSPIRE].
D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].
P. Sabella-Garnier, K. Schalm, T. Vakhtel and J. Zaanen, Thermalization/Relaxation in integrable and free field theories: an Operator Thermalization Hypothesis, arXiv:1906.02597 [INSPIRE].
A. Bukva, P. Sabella-Garnier and K. Schalm, Operator thermalization vs eigenstate thermalization, arXiv:1911.06292 [INSPIRE].
P. Günther, Huygens’ principle and hadamard’s conjecture, Math. Intel. 13 (1991) 56.
J. Écalle, Les fonctions résurgentes: (en trois parties), vol. 1, Université de Paris-Sud, Département de Mathématique, Bât. 425 (1981).
M. Mariño, Lectures on non-perturbative effects in large N gauge theories, matrix models and strings, Fortsch. Phys. 62 (2014) 455 [arXiv:1206.6272] [INSPIRE].
I. Aniceto, G. Basar and R. Schiappa, A Primer on Resurgent Transseries and Their Asymptotics, Phys. Rept. 809 (2019) 1 [arXiv:1802.10441] [INSPIRE].
D. Dorigoni, An Introduction to Resurgence, Trans-Series and Alien Calculus, Annals Phys. 409 (2019) 167914 [arXiv:1411.3585] [INSPIRE].
O. Greenberg, Generalized Free Fields and Models of Local Field Theory, Annals Phys. 16 (1961) 158.
H. Narnhofer, M. Requardt and W.E. Thirring, Quasiparticles at finite temperatures, Commun. Math. Phys. 92 (1983) 247 [INSPIRE].
L.N. Lipatov, Divergence of the Perturbation Theory Series and the Quasiclassical Theory, Sov. Phys. JETP 45 (1977) 216 [INSPIRE].
C. Mouhot and C. Villani, On Landau damping, Acta Math. 207 (2011) 29 [arXiv:0904.2760] [INSPIRE].
B. Sundborg, The Hagedorn transition, deconfinement and N = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn-deconfinement phase transition in weakly coupled large N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].
I. Amado, B. Sundborg, L. Thorlacius and N. Wintergerst, Probing emergent geometry through phase transitions in free vector and matrix models, JHEP 02 (2017) 005 [arXiv:1612.03009] [INSPIRE].
A. Jevicki and B. Sakita, The Quantum Collective Field Method and Its Application to the Planar Limit, Nucl. Phys. B 165 (1980) 511 [INSPIRE].
T. Appelquist and R.D. Pisarski, High-Temperature Yang-Mills Theories and Three-Dimensional Quantum Chromodynamics, Phys. Rev. D 23 (1981) 2305 [INSPIRE].
S.A. Hartnoll and S. Kumar, Thermal N = 4 SYM theory as a 2D Coulomb gas, Phys. Rev. D 76 (2007) 026005 [hep-th/0610103] [INSPIRE].
F.W.J. Olver et al. eds., NIST Digital Library of Mathematical Functions, release 1.0.27 of 2020-06-15 [http://dlmf.nist.gov/].
P. Banerjee, A. Gaikwad, A. Kaushal and G. Mandal, Quantum quench and thermalization to GGE in arbitrary dimensions and the odd-even effect, JHEP 09 (2020) 027 [arXiv:1910.02404] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2007.00589
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Engelsöy, J., Larana-Aragon, J., Sundborg, B. et al. Operator thermalisation in d > 2: Huygens or resurgence. J. High Energ. Phys. 2020, 103 (2020). https://doi.org/10.1007/JHEP09(2020)103
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2020)103