Instantons and the quantum bound to chaos

• URL: http://arxiv.org/abs/2212.10202v1
• Date: Tue, 20 Dec 2022 12:30:10 GMT
• Title: Instantons and the quantum bound to chaos
• Authors: Vijay Ganesh Sadhasivam, Lars Meuser, David R. Reichman, Stuart C. Althorpe
• Abstract summary: A remarkable prediction is that the associated Lyapunov exponent obeys a universal bound $lambda 2 pi k_B T/hbar$. We investigate the statistical origin of the bound by applying ring-polymer molecular dynamics to a classically chaotic double well.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Out-of-time-ordered correlators (OTOCs) can be used to quantify quantum scrambling or information loss (loosely referred to as `quantum chaos'). A remarkable prediction is that the associated Lyapunov exponent obeys a universal bound $\lambda < {2 \pi k_B T}/\hbar$. Here we investigate the statistical origin of the bound by applying ring-polymer molecular dynamics (RPMD) to a classically chaotic double well. On the timescale for exponential growth of the OTOC, RPMD is an artificial classical dynamics (in an extended phase space), which has the property of conserving the quantum Boltzmann distribution. We find that this property alone is sufficient to make the RPMD OTOC satisfy the bound, which is imposed on the chaotic RPMD trajectories by the Hessian of the imaginary-time action at the barrier instanton. Similar instantons are likely to be associated with the OTOC bound in many (perhaps all) of the diverse range of systems in which it has been observed.

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