  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.
