Out-of-time-order Correlators in Volcano potentials
The out-of-time-order correlator (OTOC) has emerged as an important diagnostic for quantum information scrambling and a key signature of quantum chaos. In this work, we discuss out-of-time-order correlators, analytically and numerically, for the so-called Volcano potentials. This family of potentials parametrically interpolates between bounded wells and confining walls, and includes Pöschl-Teller as a specific case. Through a combination of numerical diagonalization and semiclassical analysis, we investigate various regimes of the potential parameter regimes containing regions of both positive and negative curvatures. Moreover, we demonstrate in this case that short-time exponential growth of the OTOC does not necessarily signal global quantum chaos; instead, it correlates with the sampling of negative curvature regions by excited states.