Krylov complexity and oscillatory quantum dynamics in two-field inflation

We investigate Krylov-space dynamics of primordial perturbations in two-field inflation. Starting from the quadratic action for coupled curvature and entropy perturbations, we solve the mode equations with Bunch-Davies initial conditions and construct the corresponding quadratic Hamiltonian. The Gaussian quantum state is described by a four-mode squeezed state with two squeezing channels. We derive the evolution of the squeezing strength and squeezing angle and use them to evaluate the Krylov complexity, Krylov entropy, and channel-resolved Lanczos coefficients. Our numerical results show that the two channels remain weakly squeezed inside the horizon but develop different squeezing histories after horizon exit. The second channel develops strong squeezing earlier and dominates the intermediate evolution, whereas the first channel shows a delayed enhancement. The corresponding Krylov complexities exhibit distinct oscillatory structures across horizon crossing and pronounced fluctuations in the strongly squeezed superhorizon regime. These features arise from the phase-sensitive squeezing dynamics and reflect the different responses of the two channels to curvature-entropy coupling.