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

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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