Research on Quantum Field Theory for Finite Space-Time Systems and Dynamics of Quantum Systems

有限时空系统量子场论及量子系统动力学研究

基本信息

批准号：
13135221
负责人：
OHBA Ichiro
金额：
$ 4.8万
依托单位：
Waseda University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research on Priority Areas
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13135221/
关键词：
Stochastic State Diffusion Quantum-Classical Correspondence Quantum Computer of Kane's model Zeno-like Measurements Entanglement Distillation Bose-Einstein Condensation Quantum Field Theory in Finite Space Inequivalent Vacua 素粒子論量子力学基礎論

项目摘要

In this project the head investigator, I. Ohba together with Y. Ota quantized the dissipative chaos system applying the method of stochastic state diffusion, and discussed the quantum-classical correspondence quantitatively calculating pseudo-Lyapunov index. Then they developed the semiclassical approximation on the quantum dissipative system. Further, they focused on the quantum computer of nuclear spins in a semiconductor proposed by B. E. Kane, and solved the time-dependent Schrodinger equation rigorously and showed that the inevitable operation error exists in the previously proposed way of construction of the quantum gates.H. Nakazato and K. Yuasa reconsidered the quantum Zeno effect including the degrees of freedom of the environment, and found that the "environment" (of finite degrees of freedom)is purified by the Zeno-like measurement in which the frequent sequential measurements are performed on the system. As an application, they showed that the entanglement distillation and … More initialization of qubits are possible. Further, they developed the method to derive the solution of Lindlbad master equation with the Kraus representation.Y. Yamanaka together with one of the members M. Okumura considered the system of Bose-Einstein condensation of atomic gas where the translational invariance is absent due to the trapping potential for atoms, and developed its quantum field theoretical formulation. They also showed that inclusion of Goldstone mode is essential in this framework. Particularly, this formulation keeps the Ward-Takahashi identities and the degenerated vacuum is orthogonal to each other.Y. Yamanaka, M. Okumura and M. Mine showed the relation between two kinds of field theoretical methods in which the Goldstone mode is taken care of for a trapped Bose-condensed system. Further, they formulated the method in which the effect of the zero-mode on the response of trapped Bose-Einstein condensates against the external perturbation at finite temperature can be evaluated. Using this formalism, they numerically calculated its effects. Less

在这个项目中，首席研究员I.Ohba和Y.Ota应用随机状态扩散的方法量化了耗散混沌系统，并讨论了定量计算伪Lyapunov指数的量子经典对应关系，然后他们发展了半经典近似。此外，他们还重点研究了B.E.凯恩提出的半导体核自旋量子计算机，并严格求解了与时间相关的薛定谔方程，并证明了必然的结果。先前提出的量子门的构造方式存在操作错误。H. Nakazato和K. Yuasa重新考虑了包括环境自由度在内的量子芝诺效应，发现“环境”（有限自由度）通过类似 Zeno 的测量来纯化，其中在系统上执行频繁的顺序测量作为一种应用，他们表明量子位的纠缠蒸馏和初始化是可能的。此外，他们开发了导出解决方案的方法。 Y. Yamanaka 与成员之一 M. Okumura 一起考虑了原子气体的玻色-爱因斯坦凝聚系统，其中由于原子的俘获势而缺乏平移不变性，并发展了它的量子他们还表明，在这个框架中包含戈德斯通模式是至关重要的，该公式保持了 Ward-Takahashi 恒等式，并且简并真空彼此正交。 Y. Yamanaka、M. Okumura 和 M. Mine 展示了两种场论方法之间的关系，其中考虑了陷波玻色凝聚系统的戈德斯通模式，此外，他们还制定了影响该效应的方法。可以使用这种形式来评估零模式对有限温度下捕获的玻色-爱因斯坦凝聚体对外部扰动的响应的影响。