  Non-KAM (Kolmogorov-Arnold-Moser) systems, when perturbed by weak
time-dependent fields, offer a fast route to classical chaos through an abrupt
breaking of invariant phase space tori. In this work, we employ
out-of-time-order correlators (OTOCs) to study the dynamical sensitivity of a
perturbed non-KAM system in the quantum limit as the parameter that
characterizes the $\textit{resonance}$ condition is slowly varied. For this
purpose, we consider a quantized kicked harmonic oscillator (KHO) model, which
displays stochastic webs resembling Arnold's diffusion that facilitate
large-scale diffusion in the phase space. Although the Lyapunov exponent of the
KHO at resonances remains close to zero in the weak perturbative regime, making
the system weakly chaotic in the conventional sense, the classical phase space
undergoes significant structural changes. Motivated by this, we study the OTOCs
when the system is in resonance and contrast the results with the non-resonant
case. At resonances, we observe that the long-time dynamics of the OTOCs are
sensitive to these structural changes, where they grow quadratically as opposed
to linear or stagnant growth at non-resonances. On the other hand, our findings
suggest that the short-time dynamics remain relatively more stable and show the
exponential growth found in the literature for unstable fixed points. The
numerical results are backed by analytical expressions derived for a few
special cases. We will then extend our findings concerning the non-resonant
cases to a broad class of near-integrable KAM systems.
