Abstract
Recently the bound on the Lyapunov exponent in thermal quantum systems was conjectured by Maldacena, Shenker, and Stanford. If we naïvely apply this bound to a system with a fixed Lyapunov exponent , it might predict the existence of the lower bound on temperature . Particularly, it might mean that chaotic systems cannot be zero temperature quantum mechanically. Even classical dynamical systems, which are deterministic, might exhibit thermal behaviors once we turn on quantum corrections. We elaborate this possibility by investigating semiclassical particle motions near the hyperbolic fixed point and show that indeed quantum corrections may induce energy emission, which obeys a Boltzmann distribution. We also argue that this emission is related to acoustic Hawking radiation in quantum fluid. Besides, we discuss when the bound is saturated, and show that a particle motion in an inverse harmonic potential and matrix model may saturate the bound, although they are integrable.
- Received 16 May 2018
- Revised 30 January 2019
DOI:https://doi.org/10.1103/PhysRevLett.122.101603
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society