Late time dynamics in SUSY saddle-dominated scrambling through higher-point OTOC

TL;DR

This paper investigates late-time scrambling dynamics in supersymmetric quantum systems using higher-point out-of-time-order correlators, revealing their sensitivity and potential as probes for non-chaotic systems' late-time behavior.

Contribution

It provides explicit formulas for higher-point OTOCs in SUSY systems, compares bosonic and fermionic cases, and explores late-time oscillations as indicators of saddle-dominated scrambling.

Findings

Higher-point OTOCs match bosonic harmonic oscillator results.

Supersymmetry constrains OTOC dynamics across systems.

Late-time oscillations serve as probes for non-chaotic scrambling.

Abstract

In this article, we study the scrambling dynamics in supersymmetric quantum mechanical systems. The eigenstate representation of such supersymmetric systems allows us to present an explicit form of the $2N$-point out-of-time-order correlator (OTOC) using two equivalent formalisms viz. "Tensor Product formalism" and "Partner Hamiltonian formalism". We analytically compute the $2N$-point OTOC for the supersymmetric 1D harmonic oscillator and find that the result is in exact agreement with that of the OTOC of the 1D bosonic harmonic oscillator system. The higher-point OTOC is a more sensitive measure of scrambling than the usual 4-point OTOC. To demonstrate this feature, we consider a supersymmetric sextic 1D oscillator for which the bosonic partner system has an unstable saddle in the phase space, which is absent in the fermionic counterpart. For such a system we show that the bosonic, the fermionic as well as the supersymmetric OTOC exhibit similar dynamics due to supersymmetry constraints. Finally, we illustrate the late-time oscillatory behaviour of higher-point OTOC for saddle-dominated scrambling and anharmonic oscillator systems and propose it to be a probe of late-time dynamics in non-chaotic systems that exhibit fast early-time scrambling.