More on OTOCs and Chaos in Quantum Mechanics -- Magnetic Fields
Abstract
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 CT(t) = - [x(t), p]2 β and extract Lyapunov-like exponents λL that quantify early-time growth. We map out λL(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.
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