Reaching the Bound for Quantum Information Scrambling of Reactions*

Bounds such as the one discovered by Herzfeld [1] for quantum scrambling of atoms or by Maldacena [2] for many-body quantum chaos set an upper limit proportional to kT/h on the growth of Lyapunov exponents. We recently used out-of-time-order correlator (OTOC) time derivatives, quantum analogs of Lyapunov exponents in the limit of classical chaos, to show that this bound is not exceeded by quantum vibrational energy flow in molecules [3]. Here we explore quantum information scrambling in isomerization reactions modeled by an adiabatic double well either alone, bilinearly coupled to an oscillator, or bilinearly coupled to a harmonic bath. The scrambling rate is related to dynamics near saddle points in the activated dynamics regime at high temperature. This rate drastically decreases at low temperature, signal the onset of a regime the reaction takes places by tunneling, consistent with the bound on scrambling rate. We also study the effect of friction on scrambling rates in isomerization reactions by numerical and analytical treatments.

 

[1]      K. F. Herzfeld, Zur Theorie der Reaktionsgeschwindigkeiten in Gasen, Annalen der Physik 364, 635 (1919).

[2]      J. Maldacena, S. H. Shenker, and D. Stanford, A Bound on Chaos, Journal of High Energy Physics 2016, 106 (2016).

[3]      C. Zhang, P. G. Wolynes, and M. Gruebele, Quantum Information Scrambling in Molecules, Phys. Rev. A 105, 033322 (2022).