Quantum evolution speed and its limit in the driven double‐well system

Abstract We investigate quantum evolution speed in the driven double‐well system using the entangled trajectory molecular dynamics method. We emphasize not only the evolution speed of the quantum state but also its limit according to different definitions. The Wasserstein 1‐distance is used to quantify the distance between distinguishable quantum states in the phase space, the quantum speed limit based on the geometry has been shown to be the strictest one. The single trajectory's contribution to the quantum speed limit is discussed, which is related to both the time evolution of the trajectory and its position in the total Wigner function. The resonance and chaos strongly enhance the evolution speed and its limit in the driven double‐well system. The resonance effect makes a large proportion of representative points pass through the well as a whole, nevertheless, the chaos makes the Wigner function disperse in the phase space.