Oxford Condensed Matter Theory Programme Grant

凝聚态物理是一门研究物质结构和行为的学科，这些物质构成了我们日常生活中大多数常见（和不寻常）的物质。根据公认的电磁学和量子力学定律，我们理所当然地认为它们大多数是由电子和原子核相互作用组成的，并试图解释它们的性质。那么，为什么它至少和更“基础”的物理学一样有趣呢？事实证明，电子和原子核的大型组合经常表现出所谓的合作行为，这与单个部分的合作行为大不相同。例如，超导性/在足够低的温度下，某些材料的电阻基本为零的惊人事实。对这种新行为的研究需要理论方法，这些方法可以和粒子理论或相对论一样复杂。但是，虽然只有一种“万有理论”，但在中等尺度上，有许多“有效的”理论可以解释我们所观察到的丰富现象。因此，这个主题是非常多样化的。凝聚态物理已经被研究了大约100年。为什么我们希望现在取得新的进展（特别是在本提案的主题上）？至少有四个原因：1。新的实验技术使得人们能够发现一些现象，并制造出一些新材料，而这些新材料的性质是用旧方法无法解释的。与此同时，新的理论技术已经出现，它们超越了旧的方法，旧的方法只能研究弱相互作用的系统。我们的团队在这些“非微扰方法”的发展和知识方面尤其强大，这些方法适用于许多“强相关”物理学，这些物理学在现代凝聚态物质中无处不在/例如理解为什么一些材料在比预期更高的温度下变得超导；薄层电子在强磁场中的行为（量子霍尔效应）；磁性杂质在材料或“量子点”（电子被限制在其中的微小区域）中的行为；原子在低温下在阱中凝聚成单一量子态时的行为。数字计算机的速度和内存已经大大提高，我们现在可以模拟相当大而复杂的系统，很难进行分析研究。我们的团队以多种方式使用计算机，特别是研究“软”凝聚态问题，比如流体如何润湿容器壁，或者复杂流体如何移动。这些在工业过程中具有潜在的重要应用。计算机也经常被用来检查分析方法中所作近似的正确性。凝聚态理论依赖于这样一个事实：尽管这些系统是由大量的原子或电子组成的，但我们可以用统计的方式来对待它们。这是统计力学的老课题，它量化了统计波动在这种系统中的作用。最近，它的思想和方法被应用于物理学以外的许多问题，例如生物学和经济学。我们小组成员的目标不是成为这些其他领域的专家，但是，仍然存在某些问题，例如在研究市场波动或某些罕见疾病的进展方面，这些问题提供了明确的应用。

Condensed Matter Physics is the study of the structure and behaviour of the matter that makes up most of the usual (and unusual) stuff that surrounds us every day. It takes for granted that most of these are made up of electrons and nuclei interacting according to the well-established laws of electromagnetism and quantum mechanics,and tries to explain their properties.Why, then, is it at least as interesting as more 'fundamental' physics? It turns out that large assemblies of electrons and nuclei often exhibit so-called cooperative behaviour which is quite different from that of the individual parts. Superconductivity / the amazing fact that at low enough temperatures some materials have essentially zero electrical resistance, for example. The study of this new behaviour requires theoretical methods which can be every bit as sophisticated as those of particle theory or relativity. But while there is only one 'theory of everything', at intermediate scales there are any number of 'effective' theories which account for the wealth of phenomena which we observe. Thus the subject is very diverse.Condensed matter physics has been studied for about 100 years. Why do we hope to make new progress now (particularly on the subjects in this proposal)? There are at least four reasons: 1. New experimental techniques have allowed the discovery of phenomena and the construction of new materials whose properties cannot be accounted for using old ideas.2. At the same time, new theoretical techniques have become available which go beyond the older methods, which could only study systems which were weakly interacting. Our group is particularly strong in its development and knowledge of these 'non-perturbative methods,' which apply to much of the 'strongly correlated' physics which is ubiquitous in modern condensed matter / examples being the understanding of why some materials become superconducting at higher temperatures than expected; the behaviour of thin layers of electrons in strong magnetic fields (the quantum Hall effect); the behaviour of a magnetic impurity in a material, or of a 'quantum dot' / a tiny region in which electrons are confined; the behaviour of atoms in traps at low temperatures, when they condense into a single quantum state.3. The speed and memory of digital computers has increased so much that we now can simulate quite large and complicated systems, difficult to study analytically. Our group uses computers in a number of ways, in particular to study 'soft' condensed matter problems like how a fluid wets the walls of its container, or how complex fluids move. These have potentially important applications to industrial processes. Computers are also often used to check the correctness of approximations made in analytic approaches.4. Condensed matter theory relies on the fact that, although these systems are made of a large number of atoms or electrons, we can treat them in a statistical way. This is the old subject of statistical mechanics, which quantifies the role of the statistical fluctuations in such system. More recently its ideas and methods have been applied to many problems outside physics, for example in biology and economics. It is not the aim of members of our group to become experts in these other fields, but nevertheless there are certain problems, for example in studying market fluctuations, or the progress of certain rare diseases, which offer well-defined applications.