More on OTOCs and Chaos in Quantum Mechanics -- Magnetic Fields

We revisit thermal out-of-time-order correlators (OTOCs) in single-particle quantum systems, focusing on magnetic billiards. Using the stadium billiard as a testbed, we compute the thermal OTOC $C_T(t) = -\langle [x(t), p]^2 \rangle_β$ and extract Lyapunov-like exponents $λ_L$ that quantify early-time growth. We map out $λ_L(T, B)$, revealing a crossover from quantum chaos to magnetic rigidity. In parallel, we compute an alternative OTOC built from guiding-center operators, which exhibits qualitatively distinct dynamics and no exponential growth. Our results offer a controlled framework for probing scrambling, temperature dependence, and the interplay of geometry and magnetic fields in quantum systems.

💡 Research Summary

In this work the authors investigate thermal out‑of‑time‑order correlators (OTOCs) in single‑particle quantum systems subjected to a transverse magnetic field, using the stadium billiard as a prototypical chaotic geometry. The central observable is the thermal OTOC
(C_T(t)= -\langle