Krylov Complexity in Non-Inertial Quantum Systems

Abstract: In this work, we formulate the Krylov complexity in non-In an inertial quantum system, the direct emergence of the $SU(1,1)$ sector from the Klein-Gordon symplectic form dictates that the Rindler pair-number sector naturally forms the Krylov basis for uniformly accelerating observers. Under this construction, we generalize the Bogoliubov coefficients by exploiting the $SU(1,1)$ group-structured Hamiltonian. Within this framework, we explicitly derive that the Krylov complexity is exactly equal to the mean number of correlated Rindler pairs generated via Bogoliubov mixing. Furthermore, the competition between the detuning parameter and the pair-production parameter in the Hamiltonian separates the dynamics into three distinct regimes: hyperbolic Krylov spreading, critical growth, and bounded Krylov-space motion. Notably, in the detuning-dominated regime, the pair-number distribution remains exponentially confined to low Krylov levels, implying that the wave packet becomes trapped at low levels, which manifests as the localization of Krylov complexity. Ultimately, our work sheds new light on the structural construction of Krylov complexity in non-inertial quantum systems.