Low Dimensional Magnetic and Electronic Systems

9312476福勒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。该方法使用物理上可信的一维强相互作用模型的精确解，通常由Bethe Anatz求解。然而，这些所谓的可积系统的精确解往往很难物理解释，并适用于更高维的系统。将在授权期内研究的系统包括XXZ自旋链、Sine-Gordon热力学、Calogero类型系统和Toda晶格。关于这笔赠款的理论研究使用高度数学的技术来获得模型物理系统的精确解。在大多数情况下，这些精确解只能在低于我们生活的三个维度的维度中获得。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，到目前为止，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，明智地使用低维的精确解可以帮助我们理解真实物理系统的性质。尤其是高温超导体、某些介观电子器件和一般的各向异性材料。***

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. ***