Institution: Edinburgh

Assessment:  Course work 50% / Exam 50%

Course Summary

Soft Condensed Matter Physics studies complex fluids in which intermediate level structures with length scale between small molecules and the macroscopic world exist: colloidal particles, polymers, and aggregates spontaneously formed by soap-like (surfactant) molecules. This course emphasises the generic features of these systems (most importantly, Brownian motion), and develops simple models to account for their behaviour. It will also look at how the principle of soft matter physics can give insight into biological problems.

This course will explore the key principles and applications of Magnetism & Superconductivity, and their relevance to current developments in physics. The aims of this course are: 

1. To describe the key physical principles of magnetism and superconductivity 

2. To explore the theory and applications of ferromagnetism and the macroscopic behaviour of ferromagnets 

3. To explore the basic properties, phenomenology and applications of superconducting devices

From our phones to our cars to devices that diagnose medical illness, magnetism is a fundamental tool that enables modern life. This recent video by the IEEE Magnetics Society provides an overview of the applications of magnetism and why it's such an important field.   This course will cover the fundamentals of many of these concepts.

Electronic Structure Theory (SUPAEST)

Lecturer:  Andreas Hermann

Institution: Edinburgh

Hours Equivalent Credit: 20

Assessment: Problem Sheets, Project

This is a biennial course which is not offered in 2020/21, but will be running in 2021/22.

Course Summary

This course will introduce the methods and approaches used in parameter-free descriptions of the electronic structure of materials, which aim to solve the quantum mechanical many-electron problem. We will discuss underlying ground state theories, such as wave-function based correlation methods and density functional  theory, and their implementations in high-performance computing environments. We will study how to use the linear response ansatz and many-body perturbation theory to extract excited state information from those calculations, and thus accurately simulate spectroscopic and inelastic scattering experiments.  Assignments will involve calculations on realistic materials on the UK’s national supercomputers.

Lecturer: Bernd Braunecker, Jonathan Keeling
Institution: St Andrews
Hours Equivalent Credit: 18
Assessment: Continuous Assessment

This is a biennial course which will not run in 2020/21 but is expected to run in 2021/22.   

Course Summary

These lecturers cover two closely related themes: models of magnetism, and quantum phase transitions. The two parts are  strongly linked in that many of the models we will introduce to describe magnetism turn out to be paradigmatic models of quantum phase transitions. The course is intended to be relevant not just for those working on traditional solid state systems, but also those working on cold atom physics, where many of the same models and questions are also relevant.

This course is no longer offered.  

The course will provide an overview of the field of matrix product and tensor network approaches to many body systems.

Many-body systems are hindered by an exponential complexity in the number of their constituents and thus are hard to solve. Large many body systems however present exotic emerging behaviour ( such as spin liquid, superconducting and super-fluid phases) that we want to understand from first principles. Tensor networks provide a novel theoretical and computational framework to analyse collective emergence in many body systems. We will use Tensor Networks to study classical and quantum many body systems at and out-of equilibrium. The syllabus includes an introduction to the tensor network formalism and graphical notation, the recipe for describing the partition function of a classical model as the norm of a matrix product state (1D),or tensor product state (higher D).

The characterization of the properties of these states like expectation values, correlation functions, and entropies. The renormalization group in the language of tensor networks. The correspondence between statistical mechanics and quantum mechanics and some aspects of outof- equilibrium dynamics in 1 and higher dimensions. We will describe powerful numerical algorithms based on tensor networks like DMRG in 1D and its generalizations in higher D. Students are expected to have a solid background in quantum mechanics and statistical mechanics.

Assessment: Continuous Assessment

This is a biennial course, and it is not expected to run in 2020/21.  However, that decision may be revised in December.   

Response functions and Green’s functions provide a powerful mathematical language in which to describe the physics of many-body quantum systems. This course is a short introduction to them. The first few lectures define the various Green’s functions of interest, and calculate them explicitly for a few very simple systems at zero temperature. The remaining lectures give brief introductions to several more advanced topics, including Green’s functions at non-zero temperature and Green’s functions out of equilibrium. The lectures are supplemented by several problem sheets, in which the emphasis is on a strong grasp of the basics. The course is designed to be accessible to any graduate student (theoretical or experimental) who has a decent undergraduate education in quantum mechanics. Some - though not much - knowledge of the formalism of second quantisation (creation and annihilation operators) is required.
Assessment: Continuous Assessment
This is a biennial course.  It will run in 2020/21 but not in 2021/22.
This course provides an overview of theoretical concepts and tools used in contemporary research into the dynamics of interacting many-body systems. These will primarily be treated with reference to condensed matter systems driven out of equilibrium, but the relevance of the analytical techniques beyond physics (e.g. to population dynamics) will also be discussed. Upon successful completion of this course, it is intended that a student will be able to: explain the origins of stochastic dynamics and entropy production in physical systems, construct a stochastic mathematical model, such as a Boltzmann, Fokker-Planck or Langevin equation, appropriate for a given nonequilibrium system and explain how different formulations are related, write a computational algorithm to solve simple stochastic equations, such as a Fokker- Planck or Langevin equation, show how mesoscopic and macroscopic equations of motion emerge from more fundamental descriptions, analyse stochastic equations of motion to obtain predictions for emergent phenomena in nonequilibrium systems, such as fluctuationdissipation relations, phase transitions and aging, evaluate the appropriateness of stochastic modelling approaches with reference to current research in physics and other disciplines.

Assessment: Project
Institution: Heriot-Watt
Hours Equivalent Credit: 20
Assessment: Problem sheets (60%) and Final Oral Discussion (40%)

Course Summary

This course explores experimental techniques to fabricate and characterize quantum devices, with particular emphasis on systems based on individual electrons and individual spins.

1) How can we fabricate nano-devices? Growth techniques (evaporation, sputtering, molecular beam epitaxy). Lithography (optical, electron beam). Etching.

2) How can we characterize nanoscale devices? AFM, STM, SEM, TEM, optical microscopy

3) Quantum spintronic devices. Introduction to spins. Spin initialization and readout in different systems. Rabi oscillations, Ramsey interferometry, spin-echo. Spin coherence timescales. Examples from different platforms (quantum dots, nitrogen-vacancy centres in diamond).

4) introduction to superconducting devices. Basic elements of superconductivity, Josephson junctions, superconducting quantum interference devices.

Lecturer: Margherita Mazzera
Institution: Heriot-Watt
Hours Equivalent Credit: 20
Assessment: Problem Sheets and Literature Review

Course Summary
This course will focus on the theoretical description of quantum materials and related devices where the small size plays a crucial role in determining their properties and behaviours.  The fundamental aim is to provide the students with a working knowledge of contemporary theoretical nanophysics.  The course explains how nanophysical phenomena can be understood and how predictions for behaviour can be made.