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

在这个项目中，首席研究员I.Ohba和Y.Ota利用随机态扩散的方法对耗散混沌系统进行了量子化，并讨论了量子经典对应定量计算伪Lyapunov指数。然后，他们发展了量子耗散系统的半经典近似。进一步，他们重点研究了B.E.Kane提出的半导体中核自旋的量子计算机，严格求解了含时薛定谔方程，证明了先前提出的构建量子门的方法存在不可避免的操作误差。H.Nakazato和K.Yuasa重新考虑了包括环境自由度在内的量子Zeno效应，发现(有限自由度的)环境是通过对系统进行频繁的顺序测量的类Zeno测量来净化的。作为应用，他们展示了纠缠蒸馏和…量子比特的更多初始化是可能的。Y.Y.Yamanaka和M.Okumura一起研究了原子气体的玻色-爱因斯坦凝聚系统，其中由于原子的囚禁势而没有平移不变量，并发展了它的量子场理论公式。他们还表明，戈德斯通模式在这一框架中是必不可少的。特别地，该公式保持了Ward-Takahashi恒等式和简并真空相互垂直。Y.Y.Yamanaka，M.Okumura和M.MINe证明了两种场理论方法之间的关系，在这两种方法中，禁闭玻色凝聚系统的Goldstone模被处理。此外，他们还提出了一种方法，可以用来评估零模对捕获玻色-爱因斯坦凝聚体在有限温度下对外部微扰的响应的影响。使用这种形式主义，他们用数字计算了它的影响。较少

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