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 $C_T(t)=-⟨[x(t),p{]}^2{⟩}_{\beta }$ and extract Lyapunov-like exponents ${\lambda }_L$ that quantify early-time growth. We map out ${\lambda }_L(T,B)$, 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.