Noise effects on the diagnostics of quantum chaos

Abstract: This paper investigates the effects of noise on the diagnostics of quantum chaos, focusing on three primary tools: the spectral form factor (SFF), Krylov complexity, and out-of-time correlators (OTOCs). Utilizing a closed quantum system model with white noise, we demonstrate that increasing noise strength leads to an exponential suppression of these diagnostic measures. Specifically, our findings reveal that in the strong noise limit, the SFF, two-point correlation function, and OTOCs become ineffective in distinguishing chaotic behavior. The SFF is particularly impacted, exhibiting a significant decay that obscures its ability to identify quantum chaos. This study highlights the challenges posed by environmental noise in accurately diagnosing quantum chaotic systems and suggests that traditional methods may require adaptation to remain effective in realistic open quantum systems. Our results underscore the need for further research into robust diagnostic techniques that can account for noise-induced effects in quantum chaotic systems.