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

电子学与电子的运动相对应。这些电子受到作用力的操纵，这些作用力通过电子的基本电荷/e作用于这些电子。电子除了它的电荷外，还携带一个小的磁矩？，这是3d跃迁系列中磁性的主要来源。在自旋电子学中被利用的力是在瞬间起作用的吗？以及相关的角动量流。大多数非易失性存储器，例如硬盘驱动器，涉及反转磁性材料的磁区。通过这些力和电流，自旋电子学成为可能，例如，没有运动部件的硬盘驱动器。这项研究的一部分与自旋电子学的电路理论有关。构建这样的电路理论需要更好地理解磁学的微观理论。通常，例如，镍被认为是巡回铁磁体，这将由斯通纳模型来描述。然而，在Ni中观察到的自旋波意味着局域力矩的存在，而这个模型没有描述这一点。存在着涉及量子场论、Berry相的概念和所谓的奴隶玻色子的现代方法，可以用来解决这些问题。这是本文提出的研究的一个重要部分。实现室温超导将有许多重要的应用。在一定程度上，由于缺乏足够的理论理解，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，反铁磁性和超导电性是相互联系的，这一点体现在张绍强的SO(5)理论中。这将标准的BCS超导电性与反铁磁性联系在一起。另一方面，P·W·安德森提出了高温超导体中超导电性的另一种RVB理论。模型通常是用从属玻色子方法建立的。这种方法有效地将一个电子分裂成一个荷子和一个自旋，前者携带电荷e，但没有磁矩，后者携带磁矩？Holon是玻色子，而自旋是费米子。这种方法在数学上是困难的，因为要求电荷q_i=1。这里建议实际利用这一点来定义单位球。单位球上的旋转将这些玻色子和费米子混合在一起，反映了一种超对称。在由此产生的SU(3)理论中，转动现在混合了RVB超导和反铁磁性，将导致与实验不同的预测。近藤效应最初是一种隐蔽的效应，在很低的温度下发生在某些贵金属中，这些贵金属中含有非常少量的磁性杂质。这是一个困难的数学问题，根据所涉及的模型的细节，它具有许多相当奇怪的性质。同样，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。重整化组方法可以用数值或近似的方法来解决这个问题，就像过去所做的那样，并取得了相当大的成功。这些方法借用了基本粒子理论中的方法，例如，电子的电荷被重整化，即Treat是耦合常数，作为研究对象。结果是一个一阶微分方程式。另一种方法是研究质量、有效磁场，并引出一个二阶微分方程。这种方法重现了近藤问题最已知的精确结果。建议以更现代的形式采用这一办法，并将其应用于上述情况下涉及的更复杂的问题。

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.