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

TL;DR

This paper investigates thermal OTOCs in magnetic billiards, revealing how magnetic fields influence quantum chaos and scrambling, with distinct behaviors observed in different OTOC definitions and a focus on temperature and geometry effects.

Contribution

It introduces a detailed analysis of thermal OTOCs in magnetic billiards, including the computation of Lyapunov exponents and the comparison of different OTOC types, highlighting the effects of magnetic fields on quantum chaos.

Findings

Lyapunov-like exponents vary with temperature and magnetic field.

Different OTOC definitions show contrasting dynamical behaviors.

Magnetic fields induce a crossover from quantum chaos to rigidity.

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 $C_T(t) = -\langle [x(t), p]^2 \rangle_\beta$ 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.