Krylov Complexity in Non-Inertial Quantum Systems

Abstract

This study formulates observer-dependent Krylov spreading for non-inertial quantum systems driven by linear Bogoliubov transformations. Starting with the closed single Rindler-pair $SU(1,1)$ sector, we show that its Lanczos basis is identical to the Rindler pair-number basis. As a result, the Krylov spread complexity reduces exactly to the mean number of correlated Rindler pairs, $C_k=|{\beta }_k{|}^2$. Within this framework, we demonstrate that Krylov spreading dynamics are governed by the competition between the detuning parameter and the coupling constant, naturally dividing the dynamics into three distinct regimes. Notably, Krylov complexity becomes localized in the detuning-dominated regime. By extending this to a multimode, strictly quadratic Bogoliubov Hamiltonian, we find that inequivalent Rindler wave-packet pairs violate the $C_k=|{\beta }_k{|}^2$ correspondence, thereby highlighting the single-pair $SU(1,1)$ model as an exactly solvable, observer-adapted benchmark. In such multimode scenarios, the mean pair-number eigenstates no longer dictate Krylov complexity. Overall, our work provides a new perspective for analyzing Krylov complexity in non-inertial quantum systems.

29 pages, 3 figures, we have added the part of multimode Hamiltonian for illustrating the deviation between the Krylov complexity and the mean number density