The lectures are divided into two groups, the core courses and applications. Brief details about each are provided below, courses appearing alphabetically within their group. In addition to these lectures, some of the material will be backed up in a series of tutorials.

## Core courses

### CQF: Cold Matter and Quantum Fluids

Chris Hooley (St Andrews)

Sam Carr (University of Kent)

Quantum fluids are those many-particle systems in whose behaviour the effects of both the quantum mechanics and quantum statistics are important, which occurs at cold temperatures. The most important two examples are superfluids, such as liquid Helium, and superconductors. This lecture course will begin with the phenomenon of Bose condensation in an ideal Bose gas with interactions; explore why this is not a true superfluid, and go on to look at the role of interactions. It then proceeds to explore what is different when the particles are charged, and finally look at the BCS theory of superconductivity where one begins with fermions rather than bosons.

Chris is a senior lecturer at the University of St Andrews. He works on various topics in the theory of strong correlations, including non-Fermi-liquids, highly frustrated magnets, non-equilibrium atomic fluids, and vortex-mediated phase transitions.

Sam is a lecturer at the University of Kent, having previously worked in the University of Birmingham, the International Center for Theretical Physics (ICTP) in Trieste, Brookhaven National Laboratory in New York state and the University of Karlsruhe. His research focuses on strongly correlated electron systems, particularly in low-dimensions (for example, carbon nanotubes), and looking at quantum phase transitions between different ground states. He also has a strong interest in dimensional crossover phenomena, when many one-dimensional chains become weakly coupled, both in strongly anisotropic condensed matter systems, or cold atom traps.

### ELS: Electrons in Solids

Martin Lueders (Daresbury)

A quantitative understanding of bonding in condensed matter systems demands a solution of the many electron problem. This course will show how the many electron problem can be mapped onto single electron problems in an approximate way (Hartree and Hartree Fock approximations) and a formally exact way (density functional theory and the Kohn Sham equations). Further, some of the methodology used to solve the Kohn Sham equations in complex systems will be described. In the last part of the lectures, some examples will be discussed, which show how electronic structure theory was able to explain some selected phenomena.

Martin is a principal scientist at Daresbury Laboratories. His main research interests are in the field of material-specific electronic structure theory of correlated systems, including normal, superconducting and magnetic states. The aim is to develop and apply methods within the density functional theory (DFT) framework and beyond, which allow to study materials of current interest from first principles.

### SCQ: Strongly Correlated Quantum Systems

Chris Hooley (St Andrews)

This course deals mainly with the influence of interactions on the electrons in materials. We begin with a review of second quantisation and the Fermi gas theory of metals, and then progress to Landau's Fermi liquid theory and the notion of quasiparticles. The effect of impurities on the Fermi liquid (including the Kondo effect) is discussed, and we then move on to consider how the Fermi liquid gives way to other phases as the interactions are increased, concentrating on the Stoner instability and the Mott insulator. We analyse the magnetism in the Mott insulating phase, developing the concept of spin waves. Finally, we make a survey of some experimental data on strongly correlated crystalline solids, giving basic interpretations in terms of the concepts developed in the course.

Chris is a senior lecturer at the University of St Andrews. He works on various topics in the theory of strong correlations, including non-Fermi-liquids, highly frustrated magnets, non-equilibrium atomic fluids, and vortex-mediated phase transitions.

### STM: Statistical Mechanics

Richard Blythe (University of Edinburgh)

Statistical Mechanics aims to provide a macroscopic description of a physical system starting from knowledge of its microscopic properties. The methodology and techniques are widely used throughout condensed matter physics and are also today being applied to understand the dynamics of model ecologies, economies and societies. In these lectures, we will revisit the equilibrium properties of matter - such as phase transitions and universality - from the perspective of dynamics (as opposed to statics, as is typically done in undergraduate courses). Then we will examine successively further-from-equilibrium systems, ending with a discussion of fluctuations in driven systems, a subject currently generating considerable excitement in this field.

Richard is a Reader at the University of Edinburgh. Since his PhD days, he has been researching models and theories for nonequilibrium dynamical systems. Applications of these models include transport in biological systems, traffic flow, population dynamics and language change.

## Applications

### BIE: The physics of biological evolution

Bartlomiej Waclaw (School of Physics, University of Edinburgh)

The aim of this course is to discuss applications of statistical and quantum physics to the theory of Darwinian evolution. Lecture 1 will introduce basic concepts (selection, mutation, genetic drift) and simple models (Moran process) and explain how the methods of statistical physics can be applied to solve these models and derive important and quite general results. In lecture 2 we will discuss a more advanced model - the quasispecies model - and show how it can be solved in some special cases by mapping to a quantum spin chain model. Lecture 3 will discuss the role of spatial structure in biological populations of constant size, and in populations expanding into a previously unoccupied territory. The course will also highlight physicists' contribution to biological evolution. Lectures will combine PPT slides and blackboard derivations.

Bartlomiej (Bartek) Waclaw is a statistical/biological physicist from Edinburgh, and a holder of the Royal Society of Edinburgh/Scottish Government Personal Research Fellowship. He has published research articles on random matrix theory, complex networks, random walks, and spin glasses. More recently, he has been working on applications of statistical physics to biological evolution, in particular the evolution of antibiotic resistance, and cancer progression. See also http://www2.ph.ed.ac.uk/~bwaclaw/

### DFT: A Practical Guide to Density Functional Theory

Martin Lueders (Daresbury)

Density functional theory is one of the key computational techniques available today in condensed matter physics. While the theoretical background was introduced in the electrons in solids course in the first week, this short course will involve a practical session and will allow students to see for themselves how to run DFT code, and what you get out of it.

Martin is a principal scientist at Daresbury Laboratories. His main research interests are in the field of material-specific electronic structure theory of correlated systems, including normal, superconducting and magnetic states. The aim is to develop and apply methods within the density functional theory (DFT) framework and beyond, which allow to study materials of current interest from first principles.

### MES: Mesoscopic Physics and Quantum Coherence

Edward McCann (Lancaster University)

Mesoscopic physics is the name given to electronic behaviour in solid state nanostructures that are so small that their size is similar to relevant characteristic length scales. Examples of such length scales include the elastic mean free path (which governs the scale for ballistic transport), the phase coherence length (quantum interference effects), and the electronic wavelength (quantum confinement). The aim of this course is to describe key experimental transport phenomena including weak localisation, universal conductance fluctuations, Aharonov-Bohm oscillations, and conductance quantisation whilst giving an overview of theoretical methods such as the tight binding model, the Landauer-B?ttiker formulism, scattering theory, and scaling theory.

Ed McCann works in the condensed matter theory group at Lancaster University. Recently, his research has been focussed on the properties of chiral electrons in graphene and graphene multilayers, looking at their transport and spectroscopic properties.

### QIP: Quantum Information Processing

Andrew Fisher (London Centre for Nanotechnology, UCL)

Quantum Information Processing is one of the most exciting applications of modern quantum physics, and has become a flourishing interdisciplinary field in its own right. In this short course we will concentrate on some aspects of the subject most relevant to condensed matter systems. We will start by defining qubits and quantum gates, then introduce quantum operations as a model for the action of a quantum system in a noisy environment and the Kraus representation theorem which provides a composite way to represent them. Then we will move on to quantum error correction and its connection to classical codes, and briefly discuss the physics of two of the most important solid-sate qubits: impurity spins in semiconductors and superconducting circuits. Finally we will talk about two alternatives to the standard gate model of quantum computation that particularly lend themselves to solid-state systems: adiabatic quantum computation (and the related topic of quantum annealing), and the topological computation (and related topological codes).

Professor of Physics in the London Centre for Nanotechnology and the UCL Department of Physics and Astronomy; formerly Junior Research Fellow at St John's College Oxford (1989-93), Postdoctoral Fellow at the IBM Zurich Research Laboratory (1991-92), and Lecturer in Physics at the University of Durham (1993-95). He is Director of the new EPSRC Centre for Doctoral Training in Delivering Quantum Technologies, starting in 2014.

### SCM: Soft Condensed Matter

Robert Jack (Cambridge)

This course deals with the physics of soft materials. As the name suggests these materials are soft to touch (e.g. jello, creams, pastes etc.) as opposed to hard ones (e.g. metals, alloys)which fall under the purview of "Solid State Physics". An important distinction between soft materials as opposed to their hard counterparts is that entropy and not internal energy dictates their equilibrium properties. We will discuss some examples of soft-matter systems, including surfactants and colloids, concentrating particularly on phase transitions for hard colloidal spheres and rods. Then we will turn to some of the new physics that can appear in soft-matter systems that are out of equilibrium.

Rob is an Interdisciplinary Lecturer with a joint appointment between the Dept of Chemistry and DAMTP. His research involves themes from physics, chemistry and mathematics, using the theory of statistical mechanics to understand the behaviour of complex systems including biomolecules, glassy liquids, and soft matter. He is particularly interested in co-operative dynamics: for example, how do molecules move in crowded environments? What are the co-operative mechanisms for colloidal self-assembly, and the folding of biomolecules?

### TOP: Topological phases

Sam Carr (University of Kent)

The well known Landau theory of phase transitions classifies phases of matter according to broken symmetries and local order parameters, such as solids that break translational symmetry, or magnets that break magnetic rotation symmetry. It has been long known that there are phases of matter that defy this classification ? the quantum Hall state being the most obvious (but by no means only) example. With the discovery of topological insulators about 10 years ago, interest in this field has exploded, and we now know of many distinct phases of matter with no local order parameter, but instead characterised by a topological invariant. This short lecture course will focus mostly on non-interacting band theory, and introduce topological invariants, boundary states, and the bulk-boundary correspondence necessary to understand the modern topic of topological insulators. Other manifestations of topology in modern condensed matter physics will also be exposed, although not discussed in detail.

Sam is a lecturer at the University of Kent, having previously worked in the University of Birmingham, the International Center for Theretical Physics (ICTP) in Trieste, Brookhaven National Laboratory in New York state and the University of Karlsruhe. His research focuses on strongly correlated electron systems, particularly in low-dimensions (for example, carbon nanotubes), and looking at quantum phase transitions between different ground states. He also has a strong interest in dimensional crossover phenomena, when many one-dimensional chains become weakly coupled, both in strongly anisotropic condensed matter systems, or cold atom traps.