Measured Lyapunov exponent versus temperature in a quantum simulator
In plain words
OTOC experiments so far probe effectively infinite-temperature states, where quantum limits on chaos do not show. Measuring the scrambling rate in a cold many-body state would test the chaos bound directly.
Precise statement
In a quantum simulator realizing a nonintegrable lattice model (e.g. 2D Bose-Hubbard at $U/J \sim 10$ or a Rydberg array), measure the regularized thermal OTOC growth rate $\lambda_{L}(T)$ for $k_{B}T$ below the bandwidth using a time-reversal protocol. Answer: $\lambda_{L}(T)$ with error bars over a factor of 5 in T, compared with $2\pi k_{B}T/\hbar$.
What would settle it
An experiment preparing thermal states at several temperatures and extracting an exponential OTOC growth window at each.
Status in the literature
OTOC experiments to date (trapped ions, superconducting processors) probe effectively infinite-temperature or circuit states.
Parent problems
- Special case of Can a lattice with few states per site saturate the chaos bound? · open · from revision 1
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