Phase-space consideration on barrier transmission in a time-dependent variational approach with superposed wave packets

TL;DR

This paper investigates how a superposition of Gaussian wave packets in a time-dependent model describes barrier transmission, highlighting classical and quantum distinctions, and discusses challenges in accurately modeling quantum tunneling.

Contribution

It introduces a phase-space analysis of barrier transmission using superposed wave packets, clarifying the distinction between classical high-momentum effects and true quantum tunneling.

Findings

High-momentum components can cause barrier passage without tunneling

Energy conservation issues arise in different transmission and reflection channels

The model's conclusion on quantum tunneling differs from previous quick assessments

Abstract

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.