Statut  Confirmé 
Série  FORUMENS 
Domaines  condmat.statmech 
Date  Mercredi 13 Novembre 2019 
Heure  12:00 
Institut  LPENS 
Salle  Conf. IV 
Nom de l'orateur  Goldfriend 
Prenom de l'orateur  Tomer 
Addresse email de l'orateur  
Institution de l'orateur  École Normale Supérieure 
Titre  Quasiintegrable systems are slow to thermalize but may be good scramblers 
Résumé  Knowing the position of the Earth today does not enable us to predict its position 10 Myrs from now, yet, the planetary orbits in the Solar System are stable for the next 5 Gyrs [1]. This is a typical feature of classical systems whose Hamiltonian slightly differs from an integrable one  their Lyapunov time is orders of magnitude shorter than their ergodic time. This puzzling fact may be understood by considering the simple situation of an integrable system perturbed by a weak, random noise: there is no KolmogorovArnoldMoser (KAM) regime and the Lyapunov instability can be shown to happen almost tangent to the invariant tori. I will extend this analysis to the quantum case, and show that the discrepancy between Lyapunov and ergodicity times still holds, where the quantum Lyapunov exponent is defined by the growth rate of the 4point Outof TimeOrder Correlator (OTOC) [2]. Quantum mechanics limits the Lyapunov regime by spreading wavepackets on a torus. Still, the system is a relatively good scrambler in the sense that the ratio between the Lyapunov exponent and kT/\hbar is finite, at a low temperature T [3]. The essential characteristics of the problem, both classical and quantum, will be demonstrated via a simple example of a rotor that is kicked weakly but randomly. [1] J. Laskar, Chaotic diffusion in the solar system, Icarus 196, 1 (2008). [2] T. Goldfriend and J. Kurchan, Quasiintegrable systems are slow to thermalize but may be good scramblers, arXiv:1909.02145. [3] J. Maldacena, S. H. Shenker, and D. Stanford, A bound on chaos, JHEP 08, 106 (2016). 
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