Localization and Critical Phenomena in Disordered Media

将研究超导体中磁通线的性质，以及波在无序介质中的局域化、多次散射和干扰。对于第一个主题，将对第二类超导体混合态中准粒子激发的性质进行研究，以确定是否可以观察到De Haas van Alphen振荡，从而提供关于高温超导体费米面的信息。还将使用适当的变序参数对上临界场附近的无序磁通线阵的性质进行研究。我们还将研究平行于表面的外加磁场的薄膜中的磁通线的特性，以了解最近的振动簧片实验。对于第二个主题，光的局部化，将研究当散射主要是小角度散射时无序介质对光的散射。这种方法导致了一些有趣的简化。这种行为似乎受到干扰效应的支配。理解和计算这些影响是拟议研究的目标之一。%对这笔拨款进行的研究集中在凝聚态和材料物理这两个当前感兴趣的领域。在第一个领域，将研究第二类超导体中磁通线的基本性质，例如最近发现的高温超导体。虽然磁通线的性质和它们形成的结构对这些超导体的基本物理非常重要，但它们对于生产具有高电流密度的真正的超导材料也是非常重要的。第二个研究领域是波的无序局部化。人们早就知道，在无序介质中传播的电子，如非晶态半导体，可以由于材料中的本征无序而局域化。最近人们感兴趣的是无序材料对电磁波(光)局域化的发现。这为设计像半导体一样对待光的材料提供了可能性，比如处理电子。这一领域的基础研究可以对光子材料的设计和使用产生很大影响。

Research will be conducted on properties of flux lines in superconductors and on localization, multiple scattering and interference of waves in disordered media. For the first topic, investigations will be undertaken on the nature of the quasiparticle excitations in the mixed state of a type II superconductor with a view to determining whether de Haas van Alphen oscillations can be observed and thus provide information on the Fermi surface of high temperature superconductors. Research will also be undertaken on the properties of disordered flux line arrays near the upper critical field using an appropriate variational order parameter. The properties of flux lines in thin films with applied field parallel to the surface will also be studied with the objective of understanding recent vibrating reed experiments. For the second topic, localization of light, the scattering of light by a disordered medium will be studied when the scattering is predominately small angle scattering. This approach leads to some interesting simplifications. The behavior appears to be dominated by interference effects. Understanding and calculating these effects is one objective of the proposed research. %%% The research conducted on this grant focusses on two areas of current interest in condensed matter and materials physics. In the first area, the fundamental properties of magnetic flux lines in type II superconductors, such as the recently discovered high temperature superconductors, will be studied. While the properties of flux lines and the structures which they form are of basic importance to the underlying physics of these superconductors, they are also of great importance to the production of real superconducting materials which have high current densities. The second area of research is the localization of waves by disorder. It has long been known that electrons travelling in disordered media, such as an amorphous semiconductor, can be localized due to the intrinsic disorder in the material. Of more recent interest is the discovery of the localization of electromagnetic waves (light) by disordered materials. This opens up the possibility of designing materials which treats light in the same way as semiconductors, say, deal with electrons. Basic research in this area can have a large impact on the design and use of photonic materials.