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Studies of open quantum systems with applications to dissipative barrier transmission in heavy-ion fusion reactions

Tokieda Masaaki 東北大学

2021.03.25

概要

Studies of open quantum systems have attracted attentions in various fields of science, and we have seen great progress in recent years. In this thesis, we apply ideas of open quantum systems to heavy-ion fusion reactions. For theoretical description of heavy-ion fusion reactions, two different models have been used depending on the incident energy. At energies above the Coulomb barrier, importance of energy dissipation and fluctuation due to complex internal excitations has been deduced from scattering experiments. To describe them phenomenologically, the classical Langevin equation has successfully been applied to various kinds of damped nuclear collisions including fusion reactions. Whereas, it cannot be applied to fusion reactions at energies below the Coulomb barrier because fusion reactions take place thorough quantum tunneling. In that energy range, the quantum coupled-channels method with a few number of internal states has been applied, and it has succeeded in explaining sub-barrier fusion reactions. While each method succeeds in each energy range, a unified description of heavy-ion fusion reactions from sub-barrier energies to above barrier energies is beyond the reach of the current models. To achieve this, we need to incorporate dissipation and fluctuation into the formalism of quantum mechanics. It is a subject of open quantum systems, and we propose to regard heavy-ion fusion reactions as an example of open quantum systems to construct a unified model.

In this thesis, we first review the historical backgrounds in more details. Then we introduce a widely used model Hamiltonian to simulate open quantum systems, called the Caldeira-Leggett model. In this model, environment is assumed to be a collection of harmonic oscillators. As an important property relevant to our purpose, we show that it leads to the Langevin equation in the classical limit. Using this model, we deal with the following two problems in this thesis.

The first is developing a new numerical method for the model Hamiltonian. This refers to the studies of open quantum systems in the title. Following advancement of methodology in the past couple of years, we introduce a new method based on phonon number representation of a harmonic oscillator bath. To test this method, we apply it to a damped harmonic oscillator, for which the exact solution can be found easily. Through this study, we confirm the applicability of the method and show that the method can unravel how much the bath is excited in the course of the time evolution. We also find nontrivial new boson operators for a harmonic oscillator bath. Using them, we present a new perspective of the model based on relevant degrees of freedom.

The second issue is an application of the model to barrier transmission problems, including simple calculations of fusion reactions. This refers to the applications to dissi- pative barrier transmission in heavy-ion fusion reactions in the title. The aforementioned method enables one to solve scattering problems with the dissipative coupling. Taking its advantage, we consider quantum barrier transmission problems in the presence of dissipa- tion and fluctuation. To gain an insight, we first consider scattering in a one-dimensional space and explore effects of a frictional force and a random force on the transmission dy- namics. We then apply the model to a fusion problem. With the surface friction model, which has been widely used in the analysis based on the classical Langevin equation, we find suppression of fusion cross sections at sub-barrier energies and at above barrier energies. We investigate mechanisms leading to the suppression in the respective energy ranges and find out importance of dissipation during the tunneling. Based on the calcu- lation results, we discuss the need for microscopic treatments of internal excitations to achieve a unified description of fusion reactions.

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