This course will allow for advanced examination of topics related to quantum optics. Course content in any given year may vary. More than one Special Topics in Quantum Optics courses may be taken for credit and will be distinguished in each instance by a subtitle.

This course will allow for advanced examination of topics related to quantum optics. Course content in any given year may vary. More than one Special Topics in Quantum Optics courses may be taken for credit and will be distinguished in each instance by a subtitle.

This course offers an introduction to the concepts underlying nonlinear optical phenomena. Topics include: Basic formalism and classification of nonlinear optical processes through the framework of nonlinear susceptibilities: Non-phase-matched processes (e.g., rectification, Kerr effect, soliton generation, Pockels effect, two-photon absorption, degenerate four-wave mixing); phase-matched processes (parametric conversion, harmonic and difference frequency generation); Raman and Brillouin scattering. Microscopic (quantum) origin of nonlinear susceptibilities, and the use of nonlinear optics to generate nonclassical states of light. Connections between the classical and quantum regimes.

This course will be an introduction to the phenomenon of quantum entanglement, its impact upon fundamental aspects of quantum theory, and its role in diverse areas of science and technology, such as light/matter interactions, information processing and communications. The subject will be presented from a physical rather than from an information theoretic perspective, with experimental consequences and techniques being given considerable emphasis.

Topics will include: separability and entanglement; measures of entanglement; entanglement in two level systems and harmonic oscillators; physics of entangled systems; quantum communication using entanglement, entanglement and secure communication, and cluster state quantum computing.

This course builds upon the foundation established in Quantum Theory of Solids I, where the focus was on single-particle physics, including band theory. After a brief review of the topics covered in QTSI, the focus of QTSII shifts towards the exploration of strongly correlated systems characterized by significant electron-electron interactions. This advanced course delves into the profound consequences of such correlations, leading to the emergence of various phenomena. Topics covered include effects of electron-electron interactions in mean field approximations, distinguishing between band and Mott insulators, examining metal-insulator transitions, unconventional metals, exploring magnetism and magnetic materials, understanding model Hamiltonians, and studying superconductors. Students undertaking this course are expected to possess a solid background in quantum mechanics, statistical mechanics, and Quantum Theory of Solids I. By the conclusion of the course, students are anticipated to have developed a robust understanding of the effects of strong correlations in solid-state materials, enabling them to analyze and interpret complex phenomena encountered in condensed matter physics.

This course will allow for advanced examination of topics related to many-body physics. Course content in any given year may vary. More than one Special Topics in Condensed Matter course may be taken for credit and will be distinguished in each instance by a subtitle.

Topics may include: Collective modes, Importance of Symmetries and Dimensionality; Introduction to phase transitions and critical phenomena; Ginzburg-Landau theory, Mean-field theory, Critical Exponents; Goldstone modes and the lower critical dimension; Fluctuations and the upper critical dimension; Universality and self-similarity, Scaling hypothesis; Kadanoff's heuristic renormalization group and exponent identities; Perturbation theory, diagrammatic expansion; and Wilson's momentum space renormalization group, epsilon expansion, Wilson-Fisher fixed point.

Topics may include: Free fermions (bands and band topology); Linear response theory for many-body systems; Coherent state path integrals for bosons; Superfluidity and superfluid-to-Mott insulator transition; Coherent state path integrals for fermions; Density and spin response of free fermions; Interacting fermions: Collective modes.

An introduction to Quantum Field Theory and Quantum Electrodynamics. Topics include: Failure of single particle relativistic quantum mechanics, multi-particle quantum mechanics and quantum field theory, canonical quantization, symmetries and conservation laws, interacting fields and Feynman diagrams, spin 1/2 fields and the Dirac Lagrangian, gauge invariance and QED.

This course continues the study of quantum field theory started with Quantum Field Theory I into more advanced topics. Topics may include: path integral formulation of quantum field theory, loops and renormalization, the renormalization group, non-abelian gauge theories, the Higgs mechanism, anomalies, effective field theory, and effective potentials.

This course is a survey of the techniques of modern particle physics experiments; accelerators, low background laboratories and the detectors deployed there to study fundamental particles. The emphasis is on how these technologies allow us to probe new areas of particle physics. Several modern particle physics experiments will be used as examples to highlight these techniques. The basics of charged particle accelerators will be covered along with the limitations on energy and luminosity both from the point of view of accelerator technology, and the experiments. The design of low-background, underground laboratories will also be discussed and how they make it possible to study rare particle physics phenomena and search for possible dark matter candidates. The physics and technology of solid state, gas and liquid ionisation and scintillation detectors are covered, along with the practical application to identify long lived particles at accelerators or rare processes in underground labs. The physics of calorimeters and bolometers will be discussed along with the practical realization of these devices in present experiments, such as SuperCDMS and ATLAS. Innovative devices such as Cerenkov detectors will also be discussed along with their application in LHCb and the SNO+ experiment.

This course will allow for advanced examination of topics related to high-energy particle physics. Course content in any given year may vary. More than one Special Topics in Particle Physics courses may be taken for credit and will be distinguished in each instance by a subtitle.

This course will allow for advanced examination of topics related to high-energy particle physics. Course content in any given year may vary. More than one Special Topics in Particle Physics courses may be taken for credit and will be distinguished in each instance by a subtitle.

The Standard Model is the culmination of over forty years of experimental and theoretical research in particle physics. The course will provide a survey of the Standard Model, focusing on calculations by which the model can be compared to experimental results. The course will cover the construction of the Standard Model Lagrangian, phenomenology of the weak interactions, the Higgs mechanism, CP violation, Quantum Chromo Dynamics (QCD), and neutrino oscillations.

The course will focus upon the dynamics of the climate system and therefore upon the coupled evolution of the atmosphere and oceans including also the inter-linkage of these primary system components to the cryosphere and to land surface processes.

Topics may include: Solar forcing and its intrinsic temporal variability as well as it apparent variability due to variations in the Earth's orbit around the Sun; Simple energy balance models of the variations of the amplitude and phase of the seasonal cycle due to the distribution of continents and oceans; The general circulations of the atmosphere and oceans as represented by modern coupled atmosphere -ocean general circulation models; The monsoon circulations; The El Nino Southern Oscillation phenomenon; The North Atlantic Oscillation/Arctic Oscillation and the polar "annular modes"; Ice ages and paleoclimatology including the "snowball" Earth phenomenon of the deep geological past.

An overview of the fundamentals of geophysical fluid dynamics as applied to the atmosphere and ocean. Topics include dynamical scaling considering the joint effects of rotation and stratification, shallow water systems, vorticity and potential vorticity, quasigeostrophic dynamics, waves in the atmosphere and ocean, baroclinic instability, and eddy mean-flow interaction.

Review of radiative transfer; radiative absorption and emission in matter; basic molecular spectroscopy; spectral line intensities and line shapes; introduction to scattering of radiation; the role of minor constituents and the greenhouse effect; applications to the atmosphere; techniques and methodologies for atmospheric remote sounding.

Data assimilation involves combining observations with model output to obtain a consistent, evolving three-dimensional picture of the atmosphere. This process is used to generate an initial state for producing forecasts at operational weather forecast centres. Data assimilation can also provide added value to observations by filling in data gaps and inferring information about unobserved variables. In this course, common methods of data assimilation (optimal interpolation, Kalman filtering, variational methods) are introduced and derived in the context of estimation theory. A hands-on approach will be taken so that methods introduced in the lectures will be implemented in computer assignments using toy models.

This course will allow for advanced examination of topics related to earth, atmospheric, and planetary physics (EAPP). Course content in any given year may vary. More than one Special Topics in Atmospheric Physics course may be taken for credit and will be distinguished in each instance by a subtitle.

What is inverse theory in physics and geophysics? When do data-consistent models even exist? Topics may include the following: Multivariate regression modelling of discrete models, Bayesian approaches, maximum likelihood estimation, with errors and hypothesis testing, both classical and resampling(e.g. bootstrap). Continuous models where spatial resolution is a meaningful concept (Backus-Gilbert theory). The Singular Value Decomposition approach to modelling. Answerable and unanswerable questions in modelling. Singular Value Decompositions, norms such as L-1, L-infinity. Methods for non-linear modelling: e.g., Markov Chain Monte Carlo (MCMC), simulated annealing, genetic algorithms.

This course investigates the physical processes occurring in planets and moons. Topics to be covered include: the evolution of terrestrial objects (e.g., planets, moons); the equations for convection in an infinite Prandtl number fluid; planetary heat sources and thermal evolution (e.g., thermochemical convection and its surface manifestations); effects of high temperature and pressure in planetary interiors (e.g., phase changes, viscosity stratification); gravitational potential; planetary structure and global shape (e.g., gravity, rotation, composition); stress and strain in solids; regional effects on topography (e.g., lithospheric elasticity). Knowledge of vector calculus and PDEs is assumed. No previous knowledge of Earth or planetary science is required.

This foundational biophysics course focuses on the physical properties of biomolecules, with emphasis on principles of thermodynamics and statistical mechanics that are used to quantitatively describe biological structures and processes. Fundamental concepts will be introduced while making extensive use of examples from the research literature to gain an understanding of the general importance and broad applicability of physical laws to life sciences.

This course serves as the second part of the series course, building upon the foundation established in Cellular and Molecular Biophysics I.

In this course, students will explore the intricate interplay between biological entities and their dynamic environments, utilizing statistical tools to unravel the underlying patterns and principles governing these fluxes. The curriculum will delve into the statistical mechanics of biological systems, investigating how fluctuations and uncertainties at the molecular and cellular level cascade through organisms and populations. By combining theoretical frameworks with practical applications, students will develop a comprehensive understanding of how statistical dynamics can illuminate the emergent behaviors, adaptability, and resilience observed in living systems. Participants will gain the skills to quantify and model the high dimensionality and non-linearity inherent in biology, ultimately preparing them to contribute to advancements in fields across multiple scales from protein folding to microbial communities, from tissue formation to organismal physiology.

This course will provide an in depth study of the mathematical concepts, numerical methods, and computational techniques commonly employed in the study of biological physics. Topics to be covered may include stochastic processes and their applications, Monte Carlo algorithms, Bayesian inference, machine learning, molecular dynamics, and coarse-grained simulations of bio-macromolecules and their assemblies and other numerical and computational tools.

This course will provide a survey of experimental biophysical techniques. We will discuss methods that are used to examine both the structure and function of biophysical systems, from whole organisms down to single molecules. The course is intended both for students intending to work within an experimental setting and to help those with theoretical interests understand how their ideas may be validated. Topics may include laser spectroscopy, Forster resonance energy transfer (FRET), fluorescence correlation spectroscopy (FCS), confocal and multiphoton imaging, nonlinear microscopy, light sheet microscopy, super-resolved microscopy, scanning force microscopy, cryo-electron microscopy, optical and magnetic tweezers, force spectroscopy, structural characterization and molecular crystallography, nuclear magnetic resonance (NMR), as well as x-ray and neutron scattering.

This course will allow for advanced examination of topics related to biophysics. Course content in any given year may vary, but course topics may include development of tissues and organisms, learning and computation in behaviour, or emergent rules in evolution and ecology. More than one Special Topics in Biophysics course may be taken for credit and will be distinguished in each instance by a subtitle.

This course will allow for advanced examination of topics related to biophysics. Course content in any given year may vary, but course topics may include development of tissues and organisms, learning and computation in behaviour, or emergent rules in evolution and ecology. More than one Special Topics in Biophysics course may be taken for credit and will be distinguished in each instance by a subtitle.

The Report Course is taken by students in the MSc (options I and II) programme and consists of a written report of research performed in the MSc year.

MSc and PhD direct-entry candidates register in a 60x1Y Research Course in their first year of graduate study.