Dynamics of Atomic-Gas Bose-Einstein Condensates of Bose-Fermi Mixture

在微观理论的基础上对有限玻色子-费米混合凝聚体进行了理论研究，阐明了玻色子与费米子原子间相互作用引起的混合凝聚体动力学。A)随机相近似（RPA）下有限玻色-费米混合凝聚体的微观研究：我们制定并开发了RPA中有限混合物的计算机程序，用于评估有限混合物的激发能级。从结果中，我们明确了宏观计算结果的适用性，也了解了由吸引相互作用引起的不稳定性的详细结构。在强排斥相互作用下，有限混合凝聚体提出了一种新的壳层结构，费米子被推出并分布在玻色子之外。我们将RPA计算应用于壳结构凝聚态，发现了一种新的现象——单粒子费米子能级的振荡-旋转跃迁。我们还将该方法应用于准一维混合凝聚体，研究了激发谱中的Kohn异常，该异常导致凝聚体不稳定，从而产生电荷密度波。研究了准一维混合凝聚体中电荷密度波态和自旋密度波态的可能性和结构。B)有限玻色-费米混合凝聚体时间发展的模拟：我们开发并执行了模拟混合凝聚体时间发展的计算机程序。c)分子的形成和量子质量作用定律：我们估计了混合凝聚体中玻色子和费米子复合费米子（分子）的结合能。我们将化学平衡理论中的质量作用定律推广为量子统计效应定律（量子质量作用定律），并将其应用于混合冷凝物中的分子形成过程。利用这种方法，我们澄清了与分子平衡下冷凝物的相结构。D)所得结果在其他物理领域的应用：作为本研究的应用，我们研究了其他系统-正电子和夸克多体系统中的凝聚现象。这些研究还包括物理学各个领域的新方面。少

Theoretical studies have been done on finite Bose-Fermi mixed condensates on the basis of the microscopic theory, and their dynamics caused by the interatomic interaction between the boson and the fermion have been clarified.A) Microscopic studies of finite Bose-Fermi mixed condensates in random phase approximation (RPA):We have formulated and developed computer programs for finite mixtures in the RPA, Which have been performed to evaluated the excited levels of the finite mixtures. From the results, we clarified the applicability of the results obtained by macroscopic calculations, And also understood the detailed structure of the instability caused by the attractive interactions. In strong repulsive interaction, the novel shell structure has been suggested for the finite mixed condensates, where fermions are pushed out and distribute outside bosons. We applied the RPA calculation to the shell-structured condensates and found a new phenomenon-the oscillational-rotational transition in … More the one-particle fermionic levels. We also applied our method to the quasi-one-dimensional mixed condensates and studied the Kohn anomaly In the excitation spectrum, which leads to the instability of the condensates for charge-density wave creation. We studied the possibility and structures of the charge-density and spin-density wave states in quasi-one-dimensional mixed condensates.B) Simulations for time-developments of finite Bose-Fermi mixed condensates:We developed and performed the computer programs that simulate the time-developments of the mixed condensates. Using them, we studied the monopole oscillation of the mixed condensates.C) Molecular formation and Law of quantum mass action:We estimated the binding energy of the composite fermion (molecule) from boson and fermion in the mixed condensates. We extended the law of mass action used in chemical equilibrium theory into that with the quantum statistical effects (law of quantum mass action), which was applied to the molecular formation process in the mixed condensates. Using this method, we clarified the phase structure of the condensates under the equilibrium with molecules.D) Applications of the obtained results to other areas of physics:As applications of the present research, we studied the condensation phenomena in other system-positronium and quark many-body system. These researches also include new aspects in each area of physics. Less