I am currently reading the paper A Bound on Chaos.
In this paper, they evaluate the quantity C(t), which is an out-of-time-order correlator (OTOC), and use very clever arguments to show that there must be an upper bound on the Lyapunov exponent, as they have done in section 4.
My question here is that the OTOC they are considering is a 4 point 'correlation' function. In usual field theory, when we construct higher point correlation functions, they give us finer details about the system.
Similarly, if we take higher point OTOC's, by taking the commutator to the fourth power, or higher, would be get any 'finer' details of Chaotic behaviour?
In essence, I have 3 questions:
Would we get multiple Quantum Lyapunov exponents from higher point OTOC's?
What would the higher point OTOC's tell us about the chaotic behaviour of the system?
Can the higher point OTOC's be computed analytically for any system?