Krylov complexity in inverted harmonic oscillator

Understand

Recently, the out-of-time-ordered correlator(OTOC) and Krylov complexity have been studied actively as a measure of operator growth.

• OTOC is known to exhibit exponential growth in chaotic systems, which was confirmed in many previous works.
• However, in some non-chaotic systems, it was observed that OTOC shows chaotic behavior and cannot distinguish saddle-dominated scrambling from chaotic systems.
• For K-complexity, in the universal operator growth hypothesis, it was stated that Lanczos coefficients show linear growth in chaotic systems, which is the fastest.