  A known limitation of time-dependent mean-field approaches is a lack of
quantum tunneling for collective motions such as in sub-barrier fusion
reactions. As a first step toward a solution, a time-dependent model is
considered using a superposition of Gaussian wave packets, to describe the
relative motion between two colliding nuclei, which may be simplified to a
problem for one particle in one dimension. In this article, how the model
describes the potential-barrier transmission is investigated by paying
attention to the time evolution of the phase space distribution, which in
particular reveals that the behavior of the free propagation of the incoming
state is not trivial, depending on the number of superposed wave packets.
Passage over the barrier can occur due to the high-momentum components in the
incoming state corresponding to energies above the barrier height, which is,
however, of classical nature and needs to be distinguished from the true
quantum tunneling. Although a transmitted wave packet in some case may end up
with an energy lower than the barrier, a difficulty is noticed in guaranteeing
the energy conservation when the energies of different exit channels, e.g. of
transmission and reflection, are individually measured. To overcome these
issues for a description of quantum tunneling is still a challenging problem.
This article mainly treats the same system with the same model as in the paper
Phys. Lett. B 808 (2020) 135693, arXiv:2006.06944v1 by N. Hasegawa, K. Hagino
and Y. Tanimura. However, the conclusion of the present work disagrees with
their quick conclusion that quantum tunneling was simulated by the model.
Comments are made on this.
