The Generalized OTOC from Supersymmetric Quantum Mechanics-Study of Random Fluctuations from Eigenstate Representation of Correlation Functions

The concept of the out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. Further, we demonstrate an equivalent formalism of computation using a general time-independent Hamiltonian having well-defined eigenstate representation for integrable Supersymmetric quantum systems. We found that one needs to consider two new correlators apart from the usual one to have a complete quantum description. To visualize the impact of the given formalism, we consider the two well-known models, viz. Harmonic Oscillator and one-dimensional potential well within the framework of Supersymmetry. For the Harmonic Oscillator case, we obtain similar periodic time dependence but dissimilar parameter dependences compared to the results obtained from both microcanonical and canonical ensembles in quantum mechanics without Supersymmetry. On the other hand, for the One-Dimensional PotentialWell problem, we found significantly different time scales and the other parameter dependence compared to the results obtained from non-Supersymmetric quantum mechanics. Finally, to establish the consistency of the prescribed formalism in the classical limit, we demonstrate the phase space averaged version of the classical version of OTOCs from a model-independent Hamiltonian, along with the previously mentioned well-cited models.

Automated summary

The concept of the out-of-time-ordered correlation (OTOC) function is introduced as a strong theoretical probe of quantum randomness, with a general class defined to capture quantum randomness phenomena better. An equivalent formalism of computation using a general time-independent Hamiltonian for integrable Supersymmetric quantum systems is demonstrated, requiring consideration of two new correlators. By analyzing the Harmonic Oscillator and one-dimensional potential well models within the framework of Supersymmetry, distinct parameter dependences and time scales compared to non-Supersymmetric quantum mechanics are found. The consistency of the prescribed formalism in the classical limit is established through phase space averaged versions of OTOCs.