You will study advanced topics in physics and mathematics, applying the core theories and methods learned from year one and two.
You will also work on a year-long research project in a specialist area of your choice.
Advanced Quantum Theory
In this module you will apply the general theory you learnt in Introduction to Mathematical Physics to more general problems. New topics will be introduced such as the quantum theory of the hydrogen atom and aspects of angular momentum such as spin.
Atoms, Photons and Fundamental Particles
This module will introduce students to the physics of atoms, nuclei and the fundamental constituents of matter and their interactions. The module will also develop the quantum mechanical description of these.
Topics to be covered are:
- Approximation techniques first order perturbation theory, degeneracies, second order perturbation theory, transition rates, time-dependent perturbation theory, Fermi's golden rule
- Particle Physics protons and neutrons, antiparticles, particle accelerators and scattering experiments, conservation laws, neutrinos, leptons, baryons and hadrons, the quark model and the strong interaction, weak interactions, standard model
- Introduction to atomic physics review of simple model of hydrogen atom, Fermi statistics and Pauli principle, aufbau principle, hydrogenic atoms, exchange, fine structure and hyperfine interactions, dipole interaction, selection rules and transition rates
- Lasers optical polarization and photons, optical cavities, population inversions, Bose statistics and stimulated emission, Einstein A and B coefficients
- Nuclear Physics Radioactivity, decay processes, alpha, beta and gamma emission, detectors, stability curves and binding energies, nuclear fission, fusion, liquid drop and shell models.
Introduction to Solid State Physics
Solid state physics underpins almost every technological development around us, from solar cells and LEDs to silicon chips and mobile phones.
The aim of this module is to introduce to you the fundamental topics in solid state physics. We start by looking at why atoms and molecules come together to form a crystal structure. We then follow the electronic structure of these through to interesting electronic, thermal and magnetic properties that we can harness to make devices.
- Why atoms and molecules come together to form crystal structures
- The description of crystal structures, reciprocal lattices, diffraction and Brillouin zones
- Nearly-free electron model – Bloch's theorem, band gaps from electron Bragg scattering and effective masses
- Band theory, Fermi surfaces, qualitative picture of transport, metals, insulators and semiconductors
- Semiconductors – doping, inhomogeneous semiconductors, basic description of pn junction
- Phonons normal modes of ionic lattice, quantization, Debye theory of heat capacities, acoustic and optical phonons
- Optical properties of solids absorption and reflection of light by metals, Brewster angle, dielectric constants, plasma oscillations
- Magnetism – Landau diamagnetism, paramagnetism, exchange interactions, Ferromagnetism, antiferromagnetism, neutron scattering, dipolar interactions and domain formation, magnetic technology
In this module you’ll have an introduction to Einstein’s theory of general and special relativity. The relativistic laws of mechanics will be described within a unified framework of space and time. You’ll learn how to compare other theories against this work and you’ll be able to explain new phenomena which occur in relativity.
You will carry out a project drawn from one of several areas of physics. The project may be experimental or theoretical in nature. Many of the projects reflect the research interests of members of academic staff. You will work in pairs and are expected to produce a plan of work and to identify realistic goals for your project. Each pair has a project supervisor responsible for setting the project. You will also be required to maintain a diary/laboratory notebook throughout.
Occasionally the work from these projects is used in scientific publications, and the students involved are named as authors on those publications.
Depending upon the type of project that you decide to do, you will design and carry out your own experiments, theoretical calculations or computational work and use them to generate what are often new and interesting results. The project culminates in your writing a scientific report which is submitted for assessment along with your laboratory notebook.
Mathematics Group Projects
This module involves the application of mathematics to a variety of practical, open-ended problems - typical of those that mathematicians encounter in industry and commerce.
Specific projects are tackled through workshops and student-led group activities. The real-life nature of the problems requires you to develop skills in model development and refinement, report writing and teamwork. There are various streams within the module, for example:
- Pure Mathematics
- Applied Mathematics
- Data Analysis
- Mathematical Physics
This ensures that you can work in the area that you find most interesting.
In this module you will build on the foundation of knowledge gained from your core year one modules in Analytical and Computational Foundations and Calculus. You will learn to follow a rigorous approach needed to produce concrete proof of your workings.
Atmospheric and Planetary Physics
In this module you will explore the physics of planets and their atmospheres — a topic that is at the forefront of modern astrophysics and planetary science.
In the last few decades, the discovery of thousands of exoplanets beyond our Solar System has revolutionised the study of planets and their atmospheres.
Closer to home, understanding the physical processes at play in the Earth’s atmosphere remains vital for predicting weather and climate.
- Exoplanet detection methods and the physics of planet formation
- The structure, temperature and composition of planetary atmospheres
- Atmospheric dynamics
- Exoplanet atmospheres and the search for biosignatures
Nonlinear Dynamics and Chaos
How can complicated nonlinear mechanical, electrical and biological systems be understood? In this module you will develop your knowledge of classical mechanics of simple linear behaviour to include the behaviour of complex nonlinear dynamics. You’ll learn about the way in which nonlinear deterministic systems can exhibit essentially random behaviours, and approaches to understand and control them.
- In-depth knowledge of nonlinear dynamics in continuous and discrete classical systems
- Practical skills in using analytical, geometric and numerical approaches to analyse dynamics in nonlinear systems of various dimensions
- Methods to understand and create beautiful fractals through simple iteration rules.
Soft Condensed Matter
This module aims to to give you a basic grounding in key concepts in soft condensed matter physics. It will focus on the dynamic, structural and kinematic properties of these materials as well as their self-assembly into technologically important structures for the production of nanostructured materials.
Key differences and similarities between soft matter, hard matter and liquid systems will be highlighted and discussed throughout the module. Material that will be covered includes:
- Introduction to soft matter
- Forces, energies and timescales in soft matter
- Liquids and glasses
- Phase transitions in soft matter (solid-liquid and liquid-liquid demixing)
- Polymeric materials
- Crystallisation in soft systems
- Liquid crystals
- Molecular order in soft systems
- Soft Nanotechnology
This module aims to provide you with the skills necessary to use computational methods in the solution of non-trivial problems in physics and astronomy. You’ll also sharpen your programming skills through a three hour computing class and one hour of lectures per week.
Introduction to Cosmology
Cosmology is the scientific study of the Universe as a whole. It aims to understand what the Universe is made of, and its evolution from the Big Bang until today (and into the future).
- observational evidence for the Big Bang
- how the expansion of the Universe depends on its contents and geometry
- how the contents of the Universe evolve as it expands and cools
- dark matter and dark energy: observational evidence and the latest theoretical models
- inflation, a proposed period of accelerated expansion in the very early Universe
From Accelerators to Medical Imaging
Science is the cornerstone of modern healthcare. For example, in the UK’s National Health Service (NHS) more than 80% of clinical decisions are informed by scientific analysis.
In this module, we will explore some of the critical technologies that underpin these decisions. The course begins by exploring particle accelerators, and how they are used to create, for example, high energy photons or anti-matter particles. We will then see how these are used to either diagnose or treat illnesses such as cancer.
We will look closely at medical imaging techniques such as X-ray computed tomography (the CT scan), exploring the mathematics of how high-definition images of the body can be formed. We will cover nuclear medicine – how radiation can be used to track the function of organs in the body – and how advanced mathematical models feed into diagnostic decisions.
Modelling with Differential Equations
This course aims to provide students with tools which enable them to develop and analyse linear and nonlinear mathematical models based on ordinary and partial differential equations. Furthermore, it aims to introduce students to the fundamental mathematical concepts required to model the flow of liquids and gases and to apply the resulting theory to model physical situations.
In this module you will learn about the theory and applications of functions of a complex variable using a method and applications approach. You will develop an understanding of the theory of complex functions and evaluate certain real integrals using your new skills.
Functional Medical Imaging
The techniques for magnetic resonance imaging (MRI) and spectroscopy (MRS) are explored. The course aims to introduce the brain imaging technique of functional magnetic resonance imaging (fMRI), giving an overview of the physics involved in this technique. The electromagnetic techniques of electroencephalography (EEG) and magnetoencephalography (MEG) will then be outlined, and the relative advantages of the techniques described.
This course aims to extend previous knowledge of fluid flow by introducing the concept of viscosity and studying the fundamental governing equations for the motion of liquids and gases. Methods for solution of these equations are introduced, including exact solutions and approximate solutions valid for thin layers. A further aim is to apply the theory to model fluid dynamical problems of physical relevance.
Symmetry and Action Principles in Physics
Symmetry plays a central role in physics. Most of the fundamental Laws of modern physics have been formulated using symmetry principles. Symmetry is also expected to guide for further understanding and development of theories of physical phenomena.
Through a combination of lectures, engagement sessions and workshops, this module equips you with:
- the key concepts of symmetry
- the correspondence between symmetries and conservation laws
- the derivations of physics laws from the action principles
- and the consequences of symmetry breaking.
- Symmetries of space and phase space using classical mechanics
- Symmetries of spacetime and in electromagnetism using special relativity
- Main symmetry groups of modern physics laws
- How structures in nature are results of symmetry breaking.
This course introduces various analytical methods for the solution of ordinary and partial differential equations, focussing on asymptotic techniques and dynamical systems theory. Students taking this course will build on their understanding of differential equations covered in Modelling with Differential Equations.
This module explores the physical processes involved in the most extreme environments known in the Universe. Among the objects studied are neutron stars, black holes, supernova explosions, and active galactic nuclei.
Theoretical Elementary Particle Physics
Particle physics has been hugely influential in both science and society, from the discovery of the electron to the detection of the Higgs boson. In this module you will be introduced to the mathematical tools required to understand our current description of the Standard Model of particle physics.
- The Dirac equation, which describes electrons, quarks and neutrinos
- How symmetry and conservation laws are crucial in particle physics
- The Feynman approach to computing the scattering of particles
This module introduces you to the physics and applications of Semiconductors. Semiconductors are key materials of the current Information Age. They enabled most of the devices and technologies we use everyday, such as computers, internet, mobile phones. Semiconductors help us to mitigate global warming, data theft, end of the Moore’s law and other global challenges.
This module includes detailed overview of the Semiconductors past, present and future, and provides skills and knowledge essential for a future Semiconductor researcher or engineer.
- Physics and applications of conventional semiconductor materials and devices, for example p-n diodes and field-effect transistors
- Physics and applications of novel semiconductor materials, quantum materials, nanostructures, low dimensional materials, such as graphene and quantum dots
- Current and future semiconductor challenges and technologies, such as efficient solar cells, ultrasensitive phone cameras and quantum computers.
Classical and Quantum Dynamics
The course introduces and explores methods, concepts and paradigm models for classical and quantum mechanical dynamics exploring how classical concepts enter quantum mechanics, and how they can be used to find approximate semi-classical solutions.
In classical dynamics we discuss full integrability and basic notions of chaos in the framework of Hamiltonian systems, together with advanced methods like canonical transformations, generating functions and Hamiltonian-Jacobi theory. In quantum mechanics we recall Schrödinger's equation and introduce the semi-classical approximation. We derive the Bohr-Sommerfeld quantization conditions based on a WKB-approch to the eigenstates. We will discuss some quantum signatures of classical chaos and relate them to predictions of random-matrix theory. We will also introduce Gaussian states and coherent states and discuss their semi-classical dynamics and how it is related to the corresponding classical dynamics. An elementary introduction to complete descriptions of quantum mechanics in terms of functions on the classical phase space will be given.