Positive quantum Lyapunov exponents in experimental systems with a regular classical limit

TL;DR

This paper demonstrates that exponential growth of out-of-time order correlators (OTOCs) can occur in quantum systems with regular classical limits, like the Dicke and Lipkin-Meshkov-Glick models, due to unstable stationary points rather than chaos.

Contribution

It reveals that exponential OTOC growth is not exclusive to chaotic regimes but can also occur in regular systems because of unstable stationary points.

Findings

Exponential OTOC growth observed in regular regimes of the Dicke and Lipkin-Meshkov-Glick models.

Unstable stationary points, not chaos, cause exponential behavior in these models.

Experimental parameters accessible in current setups can exhibit these effects.

Abstract

Quantum chaos refers to signatures of classical chaos found in the quantum domain. Recently, it has become common to equate the exponential behavior of out-of-time order correlators (OTOCs) with quantum chaos. The quantum-classical correspondence between the OTOC exponential growth and chaos in the classical limit has indeed been corroborated theoretically for some systems and there are several projects to do the same experimentally. The Dicke model, in particular, which has a regular and a chaotic regime, is currently under intense investigation by experiments with trapped ions. We show, however, that for experimentally accessible parameters, OTOCs can grow exponentially also when the Dicke model is in the regular regime. The same holds for the Lipkin-Meshkov-Glick model, which is integrable and also experimentally realizable. The exponential behavior in these cases are due to unstable stationary points, not to chaos.