Oxford Condensed Matter Theory Programme Grant

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.