Low Dimensional Magnetic and Electronic Systems

这项研究研究了低维强相互作用的磁和电子系统，这些系统在凝聚态物理中对于理解高温超导、介观系统和各向异性材料越来越重要。该方法使用精确解，通常由Bethe Ansatz解决，一维强相互作用模型在物理上是合理的。然而，这些所谓的可积系统的精确解通常很难从物理上解释并应用于高维系统。在拨款期间将研究的系统包括XXZ自旋链、正弦戈登热力学、卡罗杰罗型系统和Toda晶格。在这项资助下进行的理论研究使用高度数学技术来获得模型物理系统的精确解。在大多数情况下，这些精确的解只能在低于我们生活的三维空间的维度中得到。因此，这些解决方案在现实世界中的适用性并不总是很清楚。另一方面，要获得三维系统的精确解几乎是不可能的，而且许多材料具有低维系统的特性。因此，明智地使用低维精确解可以帮助我们理解真实物理系统的性质。对于高温超导体、某些介观电子器件和一般的各向异性材料来说，情况尤其如此。＊＊＊

9312476 Fowler This research studies low-dimensional strongly interacting magnetic and electronic systems which are increasingly important in condensed matter physics for understanding high temperature superconductivity, mesoscopic systems and anisotropic materials. The approach uses exact solutions, usually solved by the Bethe Ansatz, of one-dimensional strongly interacting models which are physically plausible. However, the exact solutions for these so- called integrable systems are often difficult to interpret physically and apply to higher dimension systems. Systems which will be studied during the grant period include the XXZ spin chain, sine-Gordon thermodynamics, Calogero-type systems and the Toda lattice. %%% The theoretical research being done on this grant uses highly mathematical techniques to obtain exact solutions of model physical systems. In most cases, these exact solutions can only be obtained in dimensions lower than the three dimensions in which we live. Thus, the applicability of these solutions to the real world is not always clear. On the other hand, it is nearly impossible so far to obtain exact solutions of three-dimensional systems and many materials have characteristics of lower dimensional systems. Thus, judicious use of exact solutions in lower dimensions can help us understand properties of real physical systems. This is particularly the case with high temperature superconductors, certain mesoscopic electronic devices and anisotropic materials in general. ***