Study Of Thermodynamics Of Strongly Interacting Unitary Fermi Gas And Nuclear Matter

The thermodynamics of strongly interacting quantum many-particle system is a hot topic in the physics community. This dissertation study the strongly interacting Fermi gas and nuclear matter, in order to reveal the physical properties of strongly interacting quan-tum many-particle system. The study of quantum many-body theory is very challenging. The interactions in strongly correlated many-body systems are very complicated.The ultracold atomic Fermi gas and nuclear matter are two popular quantum many-body systems. In Chapter2, the research background and theoretical basis of these t-wo systems are reviewed. We first review the experiment and theoretical background of Bose-Einstein condensation and BCS-BEC crossover, then give a brief introduction to s-cattering theory and quantum mechanics of Feshbach resonance which are often used in study the ultracold atom physics. The nuclear matter properties, relativistic mean-field theory and finite temperature theory are also reviewed.Due to the scale invariance of conformal field theory, the thermodynamic laws of strongly interacting unitary Fermi gas can be similar to those of non-interacting ideal gas. For example, the virial theorem between pressure and energy density of the ideal gas P=2E/3V is still satisfied by the unitary Fermi gas. In Chapter3, the sound velocity of unitary Fermi gas with the quasi-linear approximation is analyzed. It is found that the sound velocity of unitary Fermi gas has the same form with that of the ideal Boltzmann, Bose and Fermi gas. These results further explore the universality of unitary Fermi gas.The dispersion relation of excitation mode contains a lot of information about the system. It reflects the collective properties of the system. The dispersion relation of exci-tation mode in an interacting asymmetric Fermi gas is studied in Chapter4. In the frame of the imaginary-time finite temperature field theory, the polarization tensor is calculated by taking the random phase approximation. The population imbalance effects on the dis-persion relation of excitation mode and the density-density correlation susceptibility are investigated. The numerical results in terms of the imbalance ratio indicate the polariza-tion effects on the dispersion relation and magnetic susceptibility χ.Nuclear matter is a sort of strongly interacting many-particle system. In Chapter5, we use the relativistic mean field theory to study the finite temperature nuclear matter properties. The effects of isoscalar σ-ω coupling on the equation of state (EOS) and finite temperature properties of symmetric and asymmetric nuclear matter are investigated carefully. For comparison, we also discuss the properties of two nonlinear σ self-coupling models, namely NL-SH and NL3. It is found that the σ-ω coupling term can soften the EOS, but has very limited influence to the critical temperature of the nuclear matter liquid-gas phase transition. The results can explain the astro-observation of massive neutron stars, and the calculated critical temperature of liquid-gas phase transition is under the proper region.