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

环境对宏观量子现象影响的动力学理论

基本信息

批准号：
63540269
负责人：
TSUZUKI Toshio
金额：
$ 1.28万
依托单位：
TOHOKU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1988
资助国家：
日本
起止时间：
1988 至 1989
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63540269/
关键词：
Two-state system Quantum coherence Non-adiabatic effect of the environment Quantum Langevin equation Random force and reaction field Dynamic compensation theorem Tunneling-to-localization Transitions Exact partition function スピン-ボソン系熱浴の

项目摘要

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

1)量子朗之万动力学（参考文献10）1，2，3和7）我们已经指出，除了直接场之外，反应场的同时包含对于描述玻色浴耦合的两态系统的动力学是至关重要的。这是制定在量子朗之万方程的框架中，直接场的浴被视为量子力学的随机力。我们已经详细研究了量子力学和电磁力学概念的反应场以及直接场的欧姆-德鲁德的情况下的相互作用光谱强度的浴。结果表明，Leggett等人的无相互作用的blip近似等价于完全忽略反应场的近似。我们导出了量子朗之万方程，并讨论了该方程的性质。2）自旋-玻色子系统的量子力学：动态补偿定理（参考文献1）。4，5和6）我们已经提出了 ...更多信息自旋玻色子系统基态的动力学理论。我们已经证明，对于相互作用光谱强度频率依赖性的任意正幂增量，由于位移玻色子的零点波动而产生的红外发散完全被相干激发玻色子的动力学波动所补偿。我们把这个显著的结果称为红外发散的动态补偿定理，并认为这个定理是自旋玻色子系统物理学的本质。在最低近似下求解本征值方程，我们发现存在一个相互作用强度的临界值α_c，在该值处基态经历隧穿到局域化的跃迁。在欧姆-德鲁德情况下（δ = 1），临界值为白色浴限值中的α_c = 1/2。我们进一步研究了白色浴极限下的激发光谱。3）自旋-玻色子系统的统计力学：精确配分函数（参考文献8）我们将红外发散的动态补偿定理推广到有限温度的情况。我们得到了与以往不同的精确配分函数。我们还发现低温极限下的自旋玻色子系统与近藤系统在热力学上是不等价的。少