Theoretical Researches On Nuclear Symmetry Energy And The Gen- Eralized Jaynes-Cummings Model

In this thesis we investigate several interesting questions in theoretical physics that have attracted considerable attention lately, including the nuclear symmetry in the area of nuclear physics, as well as some problems in the Jaynes-Cummings model in the area of quantum physics. The thesis is divided into two parts. In the first part, we investigate the influence of short-range-correlation between nucleons on the density-dependence of the nuclear symmetry energy at supra-saturation densities. In the second part, we investigate the mechanism behind the splitting and reunion of the Husimi Q function and a peculiar kind of pointer-state-type time evolution in a Jaynes-Cummings model with intensity-dependent level shift.The nuclear symmetry energy plays an important role in both nuclear physics and astrophysics. It affects, e.g., the existence and structure of nuclei with extreme neutron-proton ratios, the position of the proton drip line as well as the neutron drip line, the mechanism of medium energy heavy ion collision, stellar-nucleosynthesis, properties and structure of the neutron stars, etc. Due to its importance, much effort has been devoted to the study of the nuclear symmetry energy, both from the experimental side and the theoretical side. Interestingly, despite all these efforts, the behavior of the nuclear symmetry energy, especially its behavior at high density, remains largely undetermined. In the present work, with the help of the knowledge on the nucleon momentum distribution got from recent experiments, we investigate qualitatively the density dependence of the symmetry energy at supra-saturation densities.Cavity quantum electrodynamics (QED) is a thriving field with a promising per-spective to realize quantum computation, while being a perfect arena for investigating foundational questions in quantum mechanics such as non-locality and the quantum classical boundary, etc, as well as providing useful techniques for quantum communi-cation. The Jaynes-Cummings (JC) model is the most important model in the area of cavity QED, as well as the perhaps simplest one. It describes a two-level system inter-acting with a resonant or near-resonant single-mode cavity field. Despite of its simple form, it has been discovered, beyond any one’s expectation, that it can give rise to a most remarkable phenomenon, namely, the collapse and revival of the Rabi oscillation-s of the two-level system when the field is initially in a high-intensity coherent state. The correctness of the numerical calculations for this phenomenon has been long es-tablished beyond doubt, but its interpretation, namely, intuitively why does it happen, is still an open question. In this work by studying the JC model with an intensity-dependent level shift, we give a new simple transparent and reliable interpretation for this phenomenon. The JC model is also an ideal place to study physical phenomena in their simplest form. Pointer state is an important concept in the decoherence theory re-lated to the quantum mechanical measurement problem. In the standard measurement postulate, after the measurement of a certain observable, the system’s wave function collapses to one of the eigenstates of the observable, which is a pure state. In accor-dance with this heavily-verified postulate, pointer states can be defined as the states that are capable of staying disentangled from the environment despite of the nonzero interaction between them. In the present work, we show that in the JC model with an intensity-dependent level shift, there is an interesting kind of exact pointer state, which distinguishes from all known pointer states in JC-related models in that it is time-dependent. The contents of the present thesis are as follows.In chapter two we investigate the effect of short range correlation (SRC) on the density dependence of the nuclear symmetry energy at supra-saturation densities. At supra-saturation densities, the density dependence of the symmetry energy is still un-clear, and even its general trend is still controversial. In the present work, with the help of new experimental results on the nucleon momentum distribution got from re-cent experiments, we investigate qualitatively the density dependence of the symmetry energy at supra-saturation densities. Recently, experiments at the Thomas Jefferson Lab have suggested that of all the short-range correlation (SRC) pairs,90% are proton-neutron pairs, with the remaining only 10% being proton-proton and neutron-neutron pairs. This isospin dependence of the SRC has important implications for the nuclear symmetry energy. Firstly we show that there exists an interesting relation between the height of the high momentum part of the momentum distribution n(k) of finite nuclei from some state-of-the-art calculations collected from the literature and the average nucleon density. Under the assumption that this relation still holds in the infinite nucle-ar matter, we propose a simple formula which has a natural extrapolation to abnormal densities. Then we analyze the momentum distributions of symmetric nuclear matter from existing calculations in the literature and find that they share several essential features, all of which are captured correctly by our proposed formula. Finally, with-in the framework of the well-established MDI energy density functional, we calculate the density dependence of the symmetry energy using both the uncorrelated and the correlated n(k). Our study shows that, to have a realistic estimation of the relative contributions to the symmetry energy from the kinetic part and the potential part, and to further improve the accuracy in extracting information on the nuclear equation of state from medium-energy heavy ion collision data, one has to take the SRC effect into account. Also, it is further confirmed that the density dependence of the symmetry energy at supra-saturation densities is mainly determined by the competition between the SRC effect and the three-body force effect.In chapter three we describe how the mechanism of collapse and revival is demon-strated clearly in the JC model with an intensity-dependent level shift, as well as the time-dependent exact pointer state in this model. It is known that the collapse and the revival of the Rabi oscillations are associated respectively with the splitting and the re-union of the Husimi Q function. In quantum optics, the Husimi Q function is a widely used quasi-probability distribution for characterizing and visualizing the photon field. For a strong classical coherent field, it is essentially simply the complex field ampli-tude. It is of interest to see if the mechanism of Q function splitting and its relation with the collapse and revival can be demonstrated in a clearer way in the JC-extended models. In the present work, we study the tripartite relationship between the collapse and revival of the Rabi oscillation, the splitting and reunion of the Q function and the energy level structure in the JC model with an intensity-dependent level shift whose magnitude is constrained to give rise to periodic collapse and revivals. We find that within this approach all the following five important questions find a satisfactory an-swer:Why does the Q function splits into two components? During the splitting, what is each component made of? What leads to the different rotating speeds of the two components? What is the reason that the splitting and the reunion of the Q function are synchronized respectively with the collapse and the revival of the Rabi oscillations?During the collapse period, why is the population of the two-level system as a function of time so flat, that even a very careful inspection does not reveal any oscillation? It is shown that, while the collapse and the revival are associated respectively with the splitting and reunion of the Q function, as found in the previous studies, the two com-ponents of the Q function are in turn associated, in a very clear-cut way, to two sets of eigenstates, the special structure of which determines the periodic splitting and reunion of the Q function. There are strong evidences that this mechanism actually captures the situations in the paradigmatic resonant JC model quite well. We also investigate the possible physical realization of the discussed phenomena using a Rubidium atom in a cavity. Also, we show that in the JC model with an intensity-dependent level shift whose magnitude is tuned to give rise to periodic collapse and revivals of the Rabi oscillation, there exists a peculiar kind of time evolution where the two level system and the single mode boson field remain exactly disentangled throughout the evolution, in spite of the nonzero interaction between them. Interestingly, to our best knowledge, exact time-dependent pointer states as shall be discussed here has not been identified in JC-related models before. We show that the relative ease of constructing the present disentangled evolution can be attributed to the existence of a large group of degenerate eigenstates.Finally, in chapter four, we give a brief summary, and some outlooks on possible working directions in the future.