Quanum Phases in Condensed Matter

该奖项支持凝聚态物理的理论研究。该领域的一个突出问题是同时处理电子和无序环境之间的强相互作用。最近，首席研究员和合作者已经找到了一种方法，可以在大g的极限下精确地处理量子点的这两个问题，其中g是点的电导率。诀窍是使用随机矩阵理论中的技术，这些技术适用于费米能量附近的状态。在拟议的研究中，将充分探索这一进步的机会，充分利用刚刚出现的许多令人兴奋的可能性。还建议将这些技术扩展到批量系统。很多时候，我们解决难题的能力是建立在确定一个可以克服困难的小参数的基础上的。所提出的小参数1/g，将是同类中第一个有助于精确解决无序相互作用问题的参数。首席研究员将继续通过公开讲座、外展计划、评论文章和教科书编写来传播知识。这项工作有望进一步加深我们对量子点的理解，量子点是纳米技术的核心，并澄清多体物理学中非常基本的科学问题。这些拓展活动将使未来从小学到研究生的物理系学生受益。博士后研究员也将接受培训。该奖项支持凝聚态物理的理论研究。该领域的一个突出问题是电子在无序环境中的强相互作用的同时处理。在这种情况下，电子之间的相互作用是基本凝聚态物理的核心。将描述原子核状态的数学方法与纳米技术核心的“人造原子”量子点相结合，首席研究员已经开发出一种精确处理这种电子的方法。这对推进这一物理学核心问题具有很大的潜力，同时也为处理类似问题提供了新的方法。首席研究员积极参与编写教科书、评论文章和公开演讲

This award supports theoretical research in condensed matter physics. An outstanding problem in this field is the simultaneous treatment of strong interactions between electrons and a disordered environment. Recently, the principal investigator and collaborators have found a way to handle these twin problems exactly in quantum dots in the limit of large g, where g is the dot conductance. The trick is to use techniques from random matrix theory that apply to states near the Fermi energy. In the proposed research this opportunity for advancement will be fully explored, fully exploiting numerous exciting possibilities that have just opened up. It is also proposed that these techniques be extended to bulk systems.Quite often our ability to solve a difficult problem is predicated on the identification of a small parameter that tames the difficulties. The proposed small parameter, 1/g, would be the first of its kind to help in the exact solution of the disorder-interaction problem.The principle investigator will continue his work on dissemination of knowledge via public lectures, outreach programs, review articles and textbook writing. The proposed work is expected to further our understanding of quantum dots, which are at the center of nanotechnology, as well as clarify very basic scientific issues in many-body physics. The outreach activities will benefit future generations of physics students at all levels, from elementary school to graduate school. Postdoctoral associates will also be trained.%%%This award supports theoretical research in condensed matter physics. An outstanding problem in this field is the simultaneous treatment of strong interactions between electrons when they are in a disordered environment. The interplay between electrons under these circumstances is at the heart of fundamental condensed matter physics. Combining mathematics developed to describe states in the atomic nucleus with quantum dots, "artificial atoms" at the core of nanotechnology, the principal investigator has developed a way to deal with such electrons in an exact way. This has great potential to advance this core problem in physics and, at the same time, provide new methods to deal with similar problems. The principal investigator is active in writing textbooks, review articles and giving public lectures.***