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

在本课题中，首席研究员I. Ohba和Y. Ota采用随机状态扩散方法对耗散混沌系统进行了量化，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，他们着重研究了b.e. Kane提出的半导体中核自旋的量子计算机，并严格求解了随时间变化的薛定谔方程，证明了先前提出的量子门的构造方式存在不可避免的操作误差。Nakazato和K. Yuasa重新考虑了量子芝诺效应，包括环境的自由度，并发现“环境”（有限自由度）被芝诺测量净化，在芝诺测量中，对系统进行频繁的顺序测量。作为一个应用，他们证明了纠缠蒸馏和更多的初始化量子比特是可能的。进一步，他们发展了用Kraus表示导出Lindlbad主方程解的方法。Yamanaka和其中一位成员M. Okumura考虑了原子气体的玻色-爱因斯坦凝聚系统，其中由于原子的俘获势而不存在平移不变性，并发展了其量子场理论公式。他们还表明，在这个框架中包含Goldstone模式是必不可少的。特别地，这个公式保持了Ward-Takahashi恒等式和简并真空相互正交。Yamanaka， M. Okumura和M. Mine展示了两种场理论方法之间的关系，其中对捕获玻色凝聚系统的Goldstone模式进行了处理。此外，他们还提出了一种方法，该方法可以评估零模式对有限温度下捕获的玻色-爱因斯坦凝聚物对外部扰动的响应的影响。利用这种形式，他们用数值计算了它的效果。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