Non-perturbative geodesic length in JT gravity and universal time evolution of holographic complexity

The interplay between black hole interior dynamics and quantum chaos provides a crucial framework for probing quantum effects in quantum gravity. According to the holographic "Complexity=Volume" proposal, we investigated non-perturbative generating function of geodesic length in Jackiw-Teitelboim (JT) gravity to uncover universal signatures of quantum chaos and quantum complexity. We observed that the generating function interpolates between two major probes of quantum chaos - spectral form factor and complexity - highlighting its utility as a probe of chaotic spectrum in quantum gravity. Generalizing the result to general chaotic systems, we demonstrated that time evolution of the complexity is universally governed by a certain pole structure of observables, suggesting a validity of wide class of observables as a probe of quantum chaos in quantum gravity.