Study on Physical Properties of Quantum Singularity

量子奇点物理性质研究

基本信息

批准号：
16540354
负责人：
TSUTSUI Izumi
金额：
$ 2.31万
依托单位：
High Energy Accelerator Research Organization
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2007
项目状态：
已结题

项目摘要

The present study aims at providing a coherent framework for singularities in quantum mechanics and thereby seek their possible physical effects in various situations. To this end, we have investigated primarily on the three topics: (1) statistical properties of many particle systems in the presence of quantum singularity, (2) quantum singularity and quantum integrable systems, and (3) quantum singularity and quantum information.First, for (1) we have studied systems consisting of bosonic/fermionic particles confined in a quantum well in one dimension, where a quantum singularity is placed at the center of the well acting as a partition wall. Different quantum pressures emerge depending on the nature of the singularity, which is also dependent on the temperature and the number of the particles and their statistics. We have found a curious scaling law satisfied by the particle number and temperature, which suggests a novel method of detecting the nature of particles by observation of the scaling law in low temperature regimes. Concerning (2), we have considered the N = 3 Calogero model with generalized singularity in the potential, and found a new set of solutions there. This shows explicitly that physical properties do change according to the treatise of the singularity. Finally, for (3) we have proposed a simple model of quantum computation by means of quantum singularities (quantum abacus). We have also investigated the physical effects of quantum entanglement by using game theory as a testing ground. We have succeeded to provide a complete framework of two-player games in which all possible quantum strategies can be treated and yet the entanglement is transparent. The resultant Nash equilibrium can also be classified easily whereby one can observe the superiority of quantum strategies over the classical counterparts due to quantum entanglement.

本研究旨在为量子力学中的奇点提供一个连贯的框架，从而寻求它们在各种情况下可能的物理效应。为此，我们主要研究了三个主题：（1）存在量子奇点的许多粒子系统的统计特性，（2）量子奇点和量子可积系统，以及（3）量子奇点和量子信息。，对于（1），我们研究了由限制在一维量子阱中的玻色子/费米子粒子组成的系统，其中量子奇点被放置在量子阱的中心作为隔墙。根据奇点的性质，会出现不同的量子压力，而奇点的性质也取决于温度、粒子数量及其统计数据。我们发现了一个由粒子数量和温度满足的奇怪的标度律，这提出了一种通过观察低温状态下的标度律来检测粒子性质的新方法。关于（2），我们考虑了势场中具有广义奇点的 N = 3 Calogero 模型，并在那里找到了一组新的解。这明确表明物理性质确实根据奇点的论述而变化。最后，对于（3），我们提出了一个利用量子奇点（量子算盘）的简单量子计算模型。我们还通过使用博弈论作为试验场研究了量子纠缠的物理效应。我们成功地提供了一个完整的两人游戏框架，其中可以处理所有可能的量子策略，但纠缠是透明的。由此产生的纳什均衡也可以很容易地分类，由此可以观察到由于量子纠缠而导致的量子策略相对于经典策略的优越性。