Operator Size at Finite Temperature and Planckian Bounds on Quantum Dynamics

It has long been believed that dissipative timescales τ obey a "Planckian" bound τ≳(ℏ/kBT) in strongly coupled quantum systems. Despite much circumstantial evidence, however, there is no known τ for which this bound is universal. Here we define operator size at a finite temperature, and conjecture such a τ: the timescale over which small operators become large. All known many-body theories are consistent with this conjecture. This proposed bound explains why previously conjectured Planckian bounds do not always apply to weakly coupled theories, and how Planckian timescales can be relevant to both transport and chaos.Received 29 September 2018DOI:https://doi.org/10.1103/PhysRevLett.122.216601© 2019 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLocalizationString theory techniques in condensed matterTransport phenomenaPhysical SystemsStrongly correlated systemsTechniquesSachdev-Ye-Kitaev modelCondensed Matter, Materials & Applied PhysicsQuantum InformationParticles & Fields