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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，我。Ohba与Y. Ota应用随机状态扩散方法对耗散混沌系统进行量子化，并通过计算伪李雅普诺夫指数定量地讨论了量子-经典对应关系。然后他们发展了量子耗散系统的半经典近似。此外，他们专注于B提出的半导体中核自旋的量子计算机。E. Kane等人提出的量子门的构造方法，严格求解了含时薛定谔方程，并指出了在以前提出的量子门构造方法中不可避免的操作误差。Nakazato和K.汤浅重新考虑了量子芝诺效应，包括环境的自由度，并发现“环境”（有限的自由度）是由芝诺测量，其中频繁的连续测量进行系统的净化。作为一个应用，他们表明，纠缠蒸馏和 ...更多信息量子位初始化是可能的。此外，他们还发展了用克劳斯表示法推导Lindlbad主方程解的方法。山中伸弥与其中一名成员M. Okumura考虑了原子气体的玻色-爱因斯坦凝聚系统，其中由于原子的捕获势而不存在平移不变性，并发展了其量子场论公式。他们还表明，在这一框架中纳入戈德斯通模式至关重要。特别地，这个公式保持了Ward-Takahashi恒等式，并且退化真空是相互正交的. Yamanaka，M. Okumura和M. Mine指出了两种场论方法之间的关系，在这两种场论方法中，Goldstone模被用于一个被囚禁的玻色凝聚系统。此外，他们制定了方法，其中零模式对有限温度下被困玻色-爱因斯坦凝聚体对外部扰动的响应的影响可以被评估。使用这种形式主义，他们数值计算了它的影响。少