U.S.-Finland Cooperative Research on Quantum Liquid Mixtures in 2, 2+1 and 3 Dimensions

该奖项支持德克萨斯农工大学(TAMU)的埃克哈德·克罗切克教授与芬兰奥卢大学理论物理系的Mikko Saarela教授在理论物理方面进行合作。他们有两条联合研究的原则。一是在二维和三维上对均匀混合的量子流体氦-4和氦-3的结构和激发进行微观描述。他们对临界浓度、集体激发、有效质量和混合物的动态形状因子特别感兴趣。作为研究的第二条线，他们正在研究与吸附在衬底上的这些同位素元素的薄膜的对称破坏几何有关的问题。在这里，他们试图对氦-4和氦-3液体之间的界面及其集体激发进行半定量的描述。这项研究在很大程度上依赖于合作科学家的互补专业知识，这是有效分工的基础。所有关于时间相关函数的数值工作将在芬兰完成，所有关于非均匀系统的工作将在TAMU完成。关于散装混合物的工作将继续在这两个地点进行。Saarela教授已经得到了包含和优化三体关联所需的大部分结果，Krotscheck教授已经计算出环图的CBF(关联基函数)修正，目前正在研究基本图。拟议的工作建立在强相互作用多体系统理论的一般领域的富有成效的合作的基础上。对氦-3和氦-4混合物问题的彻底研究需要最先进的多体理论，这一水平超出了以前在微观尝试中理解量子液体混合物所做的工作。这项拟议的研究将有助于加强量子物理中的多体理论。它将最先进的方法应用到几个有趣的问题上，并及时与其他人正在进行的实验研究相联系，这将完善理论。

This award supports Professor Eckhard Krotscheck of Texas A & M University (TAMU) to collaborate in theoretical physics with Professor Mikko Saarela of the Department of Theoretical Physics of the University of Oulu, Finland. They have two principle lines of joint research. One is to produce a microscopic description of the structure and the excitations of uniform mixtures of the quantum fluids Helium-4 and Helium-3 in two and three dimensions. They are particularly interested in critical concentrations and in the collective excitations, the effective mass, and the dynamic form factor of the mixture. As a second line of research, they are working on questions related to the symmetry-broken geometry of films of these isotopic elements adsorbed to a substrate. Here they are seeking to produce a semi-quantitative description of the interface between the Helium-4 and the Helium-3 liquid and its collective excitation. This research relies heavily upon the complementary expertise of the collaborating scientists which is the basis for an effective division of labor. All of the numerical work on time-dependent correlation functions will be done in Finland, and all the work on non-uniform systems at TAMU. The work on bulk mixtures will continue to be done at both locations. Professor Saarela has derived most of the results necessary for the inclusion and optimization of three- body correlations, and Professor Krotscheck has worked out the CBF (correlated basis functions) corrections of ring diagrams and is presently working on the elementary diagrams. The proposed work builds on a productive collaboration in the general area of the theory of strongly interacting many-body systems. A thorough investigation of the problem of mixtures of Helium-3 and Helium-4 requires state-of-the-art many body theory at a level that is beyond what has been done previously in microscopic attempts to understand quantum liquid mixtures. The proposed research will contribute to such strengthening of many-body theory in quantum physics. It applies state-of-the- art approaches to several interesting questions and is linked in a timely fashion to experimental research being done by others which will refine the theory.