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

Abstract

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.

Chaos and complexity from quantum neural network. A study with diffusion metric in machine learning

“…Using [42,43,[58][59][60][61], one can write down the following relation between OTOC and complexity:…”

“…In general, there will be parameter sets for which this desired exponential growth and then saturation bound-like behavior cannot be observed. In these cases, to compute OTOC, one needs to explicitly compute OTOC as stated previously [58,61] and not by connecting complexity and OTOC as shown in equation (4.11). Without doing an explicit rigorous computation of the OTOC function in the present context, we want to extract the information regarding the quantum chaotic phenomena from the obtained numerical time-dependent solution of the Complexity function.…”

Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism

“…Sharing an intimate relation with the Out-Of-Time-Ordered-Correlation functions [41][42][43], abbreviated as OTOC, these two measures has been the recent tools to probe quantum randomness and chaos in various quantum mechanical systems. OTOC's which first appeared in literature in the context of superconductivity [41] soon became popular as a theoretical probe to explore the out of equilibrium phenomenon in finite temperature field theories, bulk gravitational theories and many-body quantum systems.…”

The Cosmological OTOC: A New Proposal for Quantifying Auto-correlated Random Non-chaotic Primordial Fluctuations

“…The underlying physical concept of out-of-time ordered correlation (OTOC) functions [1][2][3][4][5][6][7][8][9] within the framework of quantum field theory is considered to be a very strong theoretical tool to describe random phenomena in the quantum regime, particularly the phenomena of quantum chaos. This concept was first introduced within the framework of superconductivity to explicitly compute the vertex correction factor of current [10].…”