Krylov complexity in saddle-dominated scrambling

A bstract In semi-classical systems, the exponential growth of out-of-time-order correlator (OTOC) is believed to be hallmark quantum chaos. However, on several occasions, it has been argued that, even in integrable OTOC can grow exponentially due presence unstable saddle points phase space. this work, we probe such an system exhibiting saddle-dominated scrambling through Krylov complexity and associated Lanczos coefficients. realm universal operator hypothesis, demonstrate that coefficients follow linear growth, which ensures behavior at early times. The arises entirely saddle, dominates other phase-space away from itself. Our results reveal observed systems with thus need not