Operator thermalisation in d > 2: Huygens or resurgence
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Springer
Received: July 2, 2020 Accepted: August 16, 2020 Published: September 16, 2020
Julius Engels¨ oy,a Jorge Larana-Aragon,a Bo Sundborga and Nico Wintergerstb a
The Oskar Klein Centre for Cosmoparticle Physics & Department of Physics, Stockholm University, AlbaNova, 106 91 Stockholm, Sweden b The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark
E-mail: [email protected], [email protected], [email protected], [email protected] 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 nonperturbative 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. Keywords: 1/N Expansion, AdS-CFT Correspondence, Holography and condensed matter physics (AdS/CMT), Quantum Dissipative Systems ArXiv ePrint: 2007.00589
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)103
JHEP09(2020)103
Operator thermalisation in d > 2: Huygens or resurgence
Contents 1
2 Preliminaries 2.1 Operator thermalisation 2.1.1 Partial operator thermalisation 2.1.2 Non-thermalisation and the thermalisation hypothesis 2.1.3 Thermalisation and resurgence 2.2 Thermal singlet models
3 3 4 5 6 7
3 Thermalisation in singlet models 3.1 Low temperatures: T < TH 3.2 High temperatures: T TH 3.2.1 d = 4 3.2.2 General d > 2
9 9 10 10 11
4 Discussion
13
5 Conclusions
14
A Thermal contribution to light cone GR in any d
15
1
Introduction
Free field theories are the simplest and most prominent examples of (super-)integrable quantum field theories (QFTs), rendered exactly solvable by the existence of an infinite set of conserved charges. A direct consequence of the presence of such charges is a severely constrained time evolution even in thermal backgrounds. In particular, simple operators in free QFTs fail to satisfy the requirements of the eigenstate thermalisation hypothesis [1, 2] and their late time behaviour is therefore unlikely to approach ensemble averages, tantamount to the absence of thermalisation. Nonetheless, it is known that nontrivial interference effects can effectively mimic equilibration. For example, after quantum quenches [3–6], correlati
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