Dynamic Theory of the Influence of Environment on the Macroscopic Quantum Phenomena

1)量子朗之万动力学（参考文献1、2、3和7）我们已经指出，除了直接场之外，同时包含反应场对于描述耦合到玻色子浴的两态系统的动力学是至关重要的。这是在量子朗之万方程的框架中表述的，其中浴槽的直接场被视为量子力学随机力。我们详细研究了反应场的量子力学和统计力学概念，以及在欧姆-德鲁德情况下的直接场的相互作用光谱强度。已经证明，Leggett等人的非相互作用的光点近似等于完全忽略反应场的近似。导出了量子朗之万方程，并讨论了该方程的特征。2)自旋玻色子系统的量子力学：动态补偿定理（参考文献4、5和6）我们提出了一个关于自旋玻色子系统基态的动力学理论。我们已经证明，由于位移玻色子的零点涨落所引起的红外散度完全被相干激发玻色子的动态涨落所引起的红外散度所补偿，这是由于相互作用光谱强度的频率依赖的任意正幂delta。我们把这个显著的结果称为红外散度的动态补偿定理，并认识到这个定理是自旋玻色子系统物理学的本质。通过在最低近似下求解特征值方程，我们发现存在一个相互作用强度的临界值alpha_c，使基态经历隧穿到局域化的跃迁。在欧姆-德鲁德情况下（δ = 1）的临界值在白浴极限中为alpha_c = 1/2。我们进一步研究了白浴极限下的激发光谱。3) s自旋玻色子系统的统计力学：精确配分函数（文献8）我们将红外散度的动态补偿定理推广到有限温度的情况。我们得到了与之前不同的配分函数。我们还发现，低温极限下的自旋玻色子系统与Kondo系统在热力学上并不等效。少

1) Quantum Langevin Dynamics (Refs. 1,2,3 and 7) We have pointed out that the simultaneous inclusion of the reaction field in addition to the direct field of the bath is essentially important to describe the dynamics of the two-state system coupled to a bosonic bath. This is formulated in the framework of the quantum Langevin equation where the direct field of the bath is treated as the quantum-mechanical random force. We have studied in detail the quantum-mechanical and statistical-mechanical notions of the reaction field as well as the direct field in the Ohm-Drude case of the interaction spectral intensity of the bath. It has been shown that the non-interacting blip approximation of Leggett et al. is equivalent to the approximation of the complete neglect of the reaction field. We have derived the quantum Langevin equation and discussed about the feature of the equation.2) Quantum Mechanics of a Spin-Boson System : The Dynamic Compensation Theorem (Refs. 4,5 and 6) We have presented … More a dynamic theory of the ground state of a spin-boson system. We have shown the infrared divergence due to the zero-point fluctuation of displaced bosons is completely compensated by that due to the dynamical fluctuation of coherently excited bosons for arbitrary positive power delta of the frequency dependence of the spectral intensity of interaction. We have called this remarkable consequence as the dynamic compensation theorem of the infrared divergence and recognized that this theorem is the essence of the physics of the spin-boson system. We have found that there exists a critical value alpha_c of the interaction strength at which the ground state experiences the tunneling-to-localized transition, by solving the eigenvalue equation in the lowest approximation. The critical value in the Ohm-Drude,case (delta = 1) is alpha_c = 1/2 in the white bath limit. We have further studied the excitation spectra in the white bath limit.3) Statistical Mechanics of s Spin-Boson system : Exact Partition Function (Ref 8) We have extended the dynamic compensation theorem of the infrared divergence to the case of finite temperatures. We have obtained the exact partition function which is different from the previous ones. We have also found that the spin-boson system in the low temperature limit is not thermodynamically equivalent to the Kondo system. Less