Support for visiting fellow to perform collaborative theoretical research in spin electronics, magnetism and superconductivity

电子学对应于电子的运动。这些是由作用在这些电子上的力控制的，这是由于它的基本电荷/e。一个电子，除了它的电荷，还携带一个小的磁矩。，三维跃迁序列中磁性的主要来源。在自旋电子学中，作用在力矩上的力是什么？以及相关的角动量电流。大多数非易失性存储器，例如，硬盘驱动器，涉及磁性材料的磁畴反转。通过这些力和电流，自旋电子学使没有活动部件的硬盘驱动器成为可能。提出的部分研究与自旋电子学的电路理论有关。这种电路理论的建立需要对微观的磁性理论有更好的理解。典型地，例如，Ni被认为是一个流动的铁磁体，这将被斯通纳模型所描述。然而，对自旋波的观察，例如Ni，意味着局域矩的存在，而这个模型并没有描述。有一些涉及量子场论、贝里相概念和所谓的从属玻色子的现代方法可以用来解决这些问题。这是这里提出的研究的一个重要部分。室温超导的实现将有许多重要的应用。在某种程度上，由于缺乏足够的理论认识，室温超导体的发展受到了抑制。在目前高温超导体的背景下，反铁磁性和超导性的关系体现在张s.c.的SO(5)理论中。这将标准BCS超导性与反铁磁性联系起来。另一方面，p.w. Anderson对高温超导体中的超导性提出了另一种RVB理论。模型通常使用从属玻色子方法来表述。这种方法有效地将电子分裂成一个带电荷e但没有磁矩的holon和一个带磁矩？的自旋子。介子是玻色子，而自旋子是费米子。这种方法在数学上是困难的，因为它要求电荷Qi = 1。这里提出利用这一点来定义一个单位球。单位球Qi = 1上的旋转混合了这些玻色子和费米子，反映出一种超对称性。在由此产生的SU(3)理论中，旋转现在混合了RVB超导性和反铁磁性，并将导致关于实验的不同预测。近藤效应最初是一种模糊的效应，它发生在某些含有极少量磁性杂质的贵金属的极低温度下。这是一个很难的数学问题，根据所涉及模型的细节，它具有许多相当奇怪的性质。在自旋电子学和量子点等可能应用于量子计算的背景下，这再次成为一个重要的问题。现有的理论方法比较特殊，不能很好地适应实验中遇到的新情况。重整化群方法可以应用于这个问题，无论是数值上还是近似上，就像过去所做的那样，取得了相当大的成功。这种方法借用了基本粒子理论的方法，例如，将电子的电荷重新归一化，即将耦合常数作为研究对象。结果是一个一阶微分方程。另一种方法研究质量，有效磁场，并导致二阶微分方程。这种方法重现了大多数已知的近藤问题的精确结果。建议将这种方法以一种更现代的形式应用于上述背景下更复杂的问题。

Electronics corresponds to the movement of electrons. These are manipulated by forces which act on these electrons by virtue of its elementary charge /e. An electron, in addition to its charge, carries a small magnetic moment ?, the principal origin of magnetism in the 3d transition series. Exploited in spin electronics are the forces acting on the moment ? and the associated current of angular momentum. Most non-volatile memory, e.g., a hard drive, involves reversing magnetic domains of magnetic materials. Through these forces and currents, spin electronics makes possible, e.g., hard drives with no moving parts.Part of the research proposed has to do with a circuit theory for spin electronics. The construction of such a circuit theory requires a better understanding of the microscopic theory of magnetism. Typically, e.g., Ni is considered as an itinerant ferromagnet, which would be described by the Stoner model. However the observation of spin waves in, e.g., Ni, implies the existence of localised moments and which this model does not describe. There exist modern methods involving quantum field theories, the concept of a Berry phase, and so called slave bosons, which can be used to address these questions. This is an important part of the research proposed here. The realisation of room temperature superconductivity would have many important applications. In part, the development of room temperature superconductors is inhibited by the lack of an adequate theoretical understanding. In the context of current high temperature superconductors, that anti-ferromagnetism and superconductivity are related is embodied in the SO(5) theory due to S. C. Zhang. This connects standard BCS superconductivity with anti-ferromagnetism. On the other hand P. W. Anderson has proposed an alternative RVB theory for the superconductivity in the high temperature superconductors. Models are often formulated using the slave boson method. This method effectively splits an electron into a holon, which carries a charge e but no magnetic moment and a spinon, which carries the magnetic moment ?. The holon is a boson while the spinon is a fermion. Mathematically this method is difficult because of a requirement that a charge Qi = 1. It is proposed here to actually exploit this to define a unit sphere. Rotations on the unit sphere Qi = 1 mix these bosons and fermions reflecting a super-symmetry. In the resulting SU(3) theory, rotations mix now RVB superconductivity and anti-ferromagnetism and will lead to different predictions with respect to experiment.The Kondo effect was originally an obscure effect, which occurred at very low temperatures in certain noble metals, which contained very small amounts of magnetic impurities. It was a difficult mathematical problem that turned out to have many rather strange properties depending upon the details of the model involved. Again in the context of spin electronics and in connection with quantum dots, etc., which might find application for quantum computation, this has again become a problem of importance. The existing theoretical methods are rather special and cannot be readily be adapted to the new situations encountered in experiment. The renormalisation group approach can be applied to this problem either numerically or approximately as was done in the past with considerable success. Such approaches use methods borrowed from elementary particle theory where, e.g., the charge of the electron is renormalized, i.e., treat is the coupling constant, as the object of study. The result is a first order differential equation. Another approach studies a mass, the effective magnetic field, and leads, to a second order differential equation. This approach is reproduces most known exact results for the Kondo problem. It is proposed to put this approach in a more modern form and apply it to the more complicated problems of interest in the above context.