磁偶极-偶极相互作用(magnetic dipole-dipole interaction，MDDI)普遍存在于如电子、原子和分子等磁偶极子之间，而自旋-自旋相互作用是MDDI的一种特殊情况，理论和实验上很早已经研究表明自旋间的MDDI可以引起自旋三重态系统的零场分裂，如比较典型的氮-空位色心(nitrogen-vacancy centre，NV centre)，可以利用其零场分裂机制实现高分辨成像和单自旋测量。此外，自旋间MDDI是一类有机分子晶体中激子对发生单重态分裂(Singlet Fission，SF)的基础，而这类有机分子晶体(如红荧烯晶体、并四苯晶体等)的光转化效率可以突破传统太阳能转化材料的光转化效率，也因为发生SF过程而被做成高效率的电致发光器件。虽然早期的经典电磁理论已经给出了电偶极子和磁偶极子各自之间的偶极相互作用形式，但是随着近现代量子物理理论与技术的发展成熟，我们发现量子效应有潜在的应用价值和前景，因此，非常有必要从量子理论出发推导MDDI的理论形式。本文主要从下面三个方面开展了相关的研究工作。 第一，我们考虑由两个电子形成的自旋三重态与一个核自旋耦合的混合系统，在外加静磁场的情况下，我们研究了两个电子间MDDI的对角项与非对角项强度分别对该混合系统能谱的影响。通过直接对角化该系统哈密顿量得到的能谱表明：这两项均不仅解除了不考虑MDDI时的特殊简并，而且通过平移相关能级产生了新的交叉(避免交叉)。特别是，避免交叉能级间的能隙随着非对角项增强而变宽。为了进一步准确地说明MDDI对能级交叉(避免交叉)影响，我们计算了该系统的判别式和其中一个电子的冯诺依曼熵。最后，通过求解系统的含时薛定谔方程，我们发现在能级的避免交叉处电子自旋的极化振荡与核自旋的同相，并且平均纵向总自旋不守恒；但是在避免交叉以外的点处，自旋极化结果与避免交叉处的相反。 第二，为了进一步研究MDDI，基于量子化的电磁场，我们推导了两个非共振的多能级磁偶极子间MDDI的一般形式。由于偶极子与场的相互作用，场动力学中包含了一部分偶极场，而这部分偶极场引起了偶极子间的MDDI。和以前的研究结果不同的是：在整个推导过程中不需要旋转波近似就可以推导出非共振偶极子间的MDDI，除此之外，我们的结果还包括了反旋相互作用项、以及静态偶极子与跃迁偶极子间的混合相互作用项。从推导的结果可以看出，由场引起的相互作用受两个偶极子发出的虚/实光子影响，因此，MDDI强度与两个偶极子的跃迁频率差有关。 第三，为了更深入研究MDDI的物理机制，我们研究了有机共轭分子中激子对形成的4-电子自旋系统SF过程所影响的荧光衰减动力学，从而指导人们设计高效率的太阳能器件和电致发光器件。首先在我们选择的坐标系下重新建立了4-电子自旋哈密顿量，并改进了关于布居数演化的动力学模型，以求解包含若干相关物理过程的荧光衰减动力学。其次我们利用改进的模型模拟了Piland等人做的实验结果[G.B.Piland et al.，J.Phys.Chem.C，2013，117 1224]，该实验通过时间分辨的荧光衰减研究了粉末状红荧烯薄膜的磁效应，我们的结果显示改进的模型可以更加准确地描述真实的物理过程。从动力学模型分析可以看出，这个拟合可以反映出我们模型中涉及的真实物理过程的相对反应速率。更进一步，对于各种不同的相对分子指向和磁场指向，我们通过调查该系统的单重态投影和荧光衰减动力学发现，SF过程的荧光衰减磁场效应存在两类。 通过以上三个方面的研究，我们揭示了MDDI会对不同物理系统产生不同的物理效应，而且从理论形式上看到了更加详细的相互作用项。以这些研究结果为理论基础，可以进一步揭示和控制这些效应。 关键词：偶极-偶极相互作用；氮-空位色心；非共振偶极子；共轭有机分子；三重态激子对；磁场效应；单重态分裂动力学；交叉(避免交叉）

 The magnetic dipole-dipole interaction (MDDI) widely exists among the electrons, atoms and molecules. The spin-spin interaction is a special situation of MDDI. Long before, it was theoretically and experimentally manifested that MDDI between spins can induce the zero-field splitting in triplet system. Recently, scientists accomplished the high-resolved imaging and single-spin measurement by utilizing the zero-field splitting mechanism of the typical nitrogen-vacancy (NV) centre. In addition, the MDDI between spins is the basis that induce the singlet fission (SF) of exciton pairs in the conjugated organic molecular crystals. The efficiencies to convert solar energy in the kind of molecule, such as rubrene and tetracene crystal, can break that of the traditional solar energy material. The property also was applied to electroluminescent device with high efficiency. The theoretical forms of the dipole-dipole interaction between electric or magnetic dipoles have been perfectly obtained through early classical electromagnetic theory. However, as modem quantum physical theory and technology become mature, it can be seen that quantum effect has potential application value and prospect. Therefore, it is needed that the form of the MDDI is derived from quantum theory. The relevant research work in this thesis mainly contain three aspects as following. Firstly, we considered a hybrid system composed of a spin-1 triplet coupled to a nuclear spin. We studied the effect of the axisymmetric and the quadrupole term of the magnetic dipole interaction between the two electrons forming the triplet on the energy spectrum in a static magnetic field. The energy spectrum obtained by directly diagonalizing the Hamiltonian of the system shows that these two terms not only remove the special crossings that appear in the absence of the magnetic dipole interaction, but also produce new (avoided) crossings by lifting the relevant levels. Specially, the gaps between the avoided crossing levels increase with the strength of the quadrupole term. In order to accurately illustrate these effects, we presented the results for the discriminant and von Neumann entropy of one electron interacting with the rest of the whole system. Finally, by numerically solving the time-dependent Schrödinger equations of the system, we discovered that the polarization oscillation of electron and nuclear spin is in-phase and the total average longitudinal spin is not conserved at location of avoided crossing, but the two results are opposite beyond that. Secondly, in order to further study MDDI, we made a general derivation for the MDDI based on the mediation of the quantized electro-magnetic field. Due to the interaction with the dipoles, the dynamics of the field is added by a dipole field, which finally gives rise to the dipole-dipole interaction between two dipoles. Different from previous studies, the rotating-wave-approximation is no longer needed throughout this derivation, and our result naturally gives the interaction for non-resonant dipoles. Moreover, our derivation also gives the counter-rotating interaction terms, and even the mixed interaction terms between the permanent and transition dipoles. We noticed that this field-induced interaction is associated with the interference of the virtual/real photons emitted from the two dipoles, thus the interaction strength could be influenced by the frequency difference of the two dipoles. Thirdly, in order to again study the physical mechanism of MDDI, we investigate the FD dynamics induced by SF of 4-spin system formed by exciton pair in conjugated organic molecules, providing the guide to design the high-efficiency photovoltaic and electroluminescent devices. Firstly, we rebuilt the four-electron spin Hamiltonian under coordinate system chosen by us and presented an improved model described by the population evolution equations on the FD dynamics that contain several relevant physical processes. The improved model for total random molecular orientation gives a more consistent fitting on the experimental data [G. B. Piland et al., J. Phys. Chem. C, 2013, 117 1224] about time-resolved FD of amorphous rubrene thin films in the presence of strong magnetic field. The fitting can reflect the relative rates of the real physical processes. Further on, our results show two kinds of magnetic field effect for the variety of two molecular relative orientations with respect to each other and the magnetic field by investigating the singlet projection and FD dynamics of the system. According to above studies, we know that MDDI can induce different effects in many physical system, and the all interaction terms from the forms of MDDI. It provides the basis for further revealing and controlling these effects. Key Words: dipole-dipole interaction; nitrogen-vacancy color center; non-resonant dipoles; conjugated organic molecules; triplet pair excitons; magnetic field effect; singlet fission dynamics; (avoided) crossings