Exploration of classical-quantum and easy-hard boundaries

经典量子和易难边界的探索

• 批准号: 1314748
• 负责人: Tzu-Chieh Wei
• 金额: $ 18万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1314748&HistoricalAwards=false
• 关键词: Exploration; classical; quantum; easy; hard

A quantum spin, like a classical magnet, can point at any direction, but a collection of quantum spins generally behave in a more exotic way and can point to many more directions than classical spins do. This usually translates to the feature that quantum many-body problems are much harder than classical problems. However, in some physical models, quantum spins, even though they can point to more directions (which originate from large spin magnitudes), turn out to behave much like classical magnets, with only small fluctuations around the direction they point to. It seems that even in the quantum world, there are regions that look more or less like the classical world. Where is the boundary between the classical and quantum territories? When do quantum problems become easy and when do they become hard? These two intimately related questions are the subject of this project. A clear characterization of such a `transition' will help to understand the exotic properties of quantum many-body systems.The integration of the research findings of this project into education on quantum information and quantum many-body physics will help to nurture a new generation of students with new tools of thinking. This project also includes training of a graduate student and mentoring of a postdoctoral researcher. The planned outreach activities such as giving public lectures, mentoring high school students for summer research projects, and developing materials and activities for high school students in science and mathematics education will complement the research activities and lead to sustaining impacts.

量子自旋就像经典磁铁一样，可以指向任何方向，但量子自旋的集合通常以更奇特的方式表现，可以指向比经典自旋更多的方向。这通常转化为量子多体问题比经典问题难得多的特征。然而，在一些物理模型中，量子自旋，即使它们可以指向更多的方向（这源于大的自旋幅度），结果表现得很像经典磁铁，在它们指向的方向上只有很小的波动。似乎即使在量子世界中，也有一些区域看起来或多或少与经典世界相似。经典领域和量子领域的界限在哪里？量子问题何时变得容易，何时变得困难？这两个密切相关的问题是本项目的主题。对这种“跃迁”的明确描述将有助于理解量子多体系统的奇异性质，将本项目的研究成果融入量子信息和量子多体物理学教育，将有助于培养具有新思维工具的新一代学生。该项目还包括培训一名研究生和指导一名博士后研究员。计划开展的外联活动，如举办公开讲座、指导高中生开展暑期研究项目以及为高中生编写科学和数学教育材料和开展活动，将补充研究活动并产生持续影响。