Modules Offered (for cohort before AY2021/22)

Prerequisite & Preclusion(s): please refer to NUSMODS

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Brief Description of Modules

PC5101 Physics and Technology

This is a new module which aims to highlight the relevance and importance of physics in many aspects of technology. It aims to serve as the overview module to expose the students to a few key technological development when Physics plays a vital role. This module will be conducted by our own lecturers. The selected topics will be current and directly relevant to the potential career options that the MSc students will be considering. Discussion of each topic shall cover the basic physics principles leading to the state of the art development in the technology. The duration on each topic can last from 2 weeks to 3 weeks. Examples of the topics include energy and batteries, solar energy systems, quantum technologies, computer modelling in Physics, sensor devices, communication systems, microelectronics, advanced functional materials, biophysical instruments, etc.

PC5102 Physics Practices in Industry

This is a new lecture module covering a series of lecture clusters/seminars in industrial physics co-taught by our lecturers and our industrial partners and collaborators. Students will be exposed to the multiple-faceted career option that a physicist can choose in the industry. Our industrial partners will provide an overview of a certain industrial sector and share their experience on the role a physicist plays in this sector. Our partners shall also emphasize on the important skillsets to learn in order to be well-prepared for the career chosen. The range of industrial sector shall cover Semiconductor MNC, Engineering, Material Science, IT, Finance, Data Sciences, Health Science. Medical Physics, Energy Sector etc. Note: The list of potential industrial partners and collaborators include: AI: Industrial Partner, Applied Materials, Global Foundries, Bruker Nano Surface Division, IOT, Orolia, IHPC, DSTA, SepQtral, LightHaus, NCCS, Illumina.

PC5198 Graduate Seminar Module in Physics

This is a required module for all research Masters and PhD students admitted from AY2004/2005. The main purpose of this module is to help graduate students to improve their presentation skills and to participate in scientific seminars/exchanges in a professional manner. The activities of this module include giving presentations during the lecture hours and attending seminars organised by the Department. Students are also required to write summaries of some departmental seminars attended. The grade of this module will be “Satisfactory/Unsatisfactory” based on student’s talk presentations, participation of seminars and the summary writing.

PC5201 Advanced Quantum Mechanics

This module is an introduction to advanced topics in quantum theory. Topics include applications in many-body systems; Scattering theory; Approximation methods and their applications. General description of relativistic equations and their solutions; Interaction with electromagnetic fields; Path integral formulation of quantum mechanics. This module is targeted at all students undertaking graduate studies.

PC5202 Advanced Statistical Mechanics

This module presents an introduction to phase transitions and fluctuations. For phase transitions, the course starts with the treatment of Landau and mean field. Exact Ising model results are then discussed. Critical exponents are introduced and their relations obtained using the scaling hypothesis and Kadanoff’s scheme. Real space renormalization is then used to show how the critical exponents can be calculated. For fluctuations, Langevin, Fokker-Planck equations will be used. Time dependence and fluctuation dissipation theorem then follow. Brownian motion will be used as an example. This module is targeted at physics graduate students with at least one year of statistical mechanics.

PC5203 Advanced Solid State Physics

This module aims to give graduate students additional training in the foundations of solid state physics and is intended to prepare them for research work and other graduate coursework modules. Topics to be covered include: translational symmetry and Bloch’s theorem, rotational symmetry and group representation, electron-electron interaction and Hartree-Fock equations, APW, OPW, pseudopotential and LCAO schemes of energy band calculations, Boltzmann equation and thermoelectric phenomena, optical properties of semiconductors, insulators and metals, origin of ferromagnetism, models of Heisenberg, Stoner and Hubbard, Kondo effect. Students are expected to read from a range of recommended and reference texts, and will be given an opportunity to present their reading as part of the regular lessons.

PC5204 Special Topics in Physics: Magnetic Materials and Applications

This module presents special selected topics of current interest. For this academic year, the module aims to introduce novel magnetic phenomena in solids with emphasis on physics and applications of spin based electronics or spintronics. The topics covered include general introduction to magnetism, exchange interactions in magnetic solids, band structure, half metals, dilute magnetic semiconductors, spin dependent electrical transport, spin polarization & detection, magneto transport in multilayers, oxides & magnetic semiconductors, magnetic nanostructures and spin injection across various interfaces. Other spin dependent phenomena such as magneto caloric, magneto elastic, magneto impedance and magnetic resonance effects will also be discussed. Application of spintronics in novel devices including GMR read heads, MRAM, spinFET, spin transistor, magnetic sensors for strain & bio-molecule detection will be illustrated. This module is targeted at postgraduate students of physics, engineering and materials science who have basic knowledge in magnetism and solid state physics/devices.

PC5204B Special Topics in Physics: Analytic Approximations

This module covers advanced mathematical methods for obtaining approximate analytical solutions to physical problems. It is designed to help graduate students build the skills necessary to analyse equations, integrals, and series that they encounter in their research. Topics include local analysis of differential equations, asymptotic expansion of integrals, and summation of series.

PC5205 Topics in Surface Physics

Selected topics from the following will be covered: introduction to surfaces in ultrahigh vacuum; thermodynamic and statistical properties of clean surfaces; interactions between light/ion/electron beams with surface and the surface analysis techniques derived from (including XPS, UPS, IR/Raman, RBS, SIMS, Auger, STM/AFM etc.); electronic, magnetic and optical properties at the surface; surface science in thin films, nanostructures and biomaterials; adsorption phenomena at surfaces; surface processes on nucleation and epitaxial growth; catalysis etc. There are laboratory sessions in this module which contains practice on XPS, SIMS, STM/AFM and IR. This module is targeted at physics, chemistry, materials science and engineering students who already have a basic knowledge of solid-state physics.

PC5206 Selected Topics in Quantum Field Theory

This is an advanced module for students of theoretical physics. The topics covered are: Second quantization and path integral formulation of quantum field theory, Feynman rules for scalar, spinor, and vector fields, renormalization and symmetry, renormalization group, and connection with condensed matter physics.

PC5207 Topics in Optical Physics

The module aims to provide a comprehensive understanding on the principles of nonlinear optics. The module is targeted at postgraduate students who have acquired a background in optics, and who are involved in optics-related studies and research. The module presents the principles of nonlinear optics and photonics devices, which includes: nonlinear optical susceptibility, wave propagation in nonlinear media; sum and difference frequency generation, parametric amplification and oscillation, photonic crystals; phase conjugation, optical-induced birefringence, self-focusing, nonlinear optical absorption, photonic devices; ultrafast laser.

PC5209 Accelerator Based Materials Characterisation

The course gives an introduction to the physics of ion beam analysis. After a general introduction, inter-atomic potentials, cross sections and stopping powers are discussed, and the theory of the stopping process is developed based on the Thomas-Fermi statistical atom. Accelerators and other instrumentation are introduced, and a range of analytical techniques is discussed in detail: Rutherford Backscattering (RBS), Proton Induced X-ray Emission (PIXE), Elastic Recoil Detection Analysis (ERDA), Nuclear Reaction Analysis NRA, and Accelerator Mass Spectrometry (AMS). Finally, the more specialised fields of Nuclear Microscopy and Synchrotron radiation are discussed.

PC5210 Advanced Dynamics

The module aims to understand Lagrangian mechanics, Hamiltonian mechanics, and basic ideas of nonlinear dynamics and chaos. Topics discussed are: variational principle and Lagrangian mechanics, Hamiltonian mechanics, the Hamiltonian formulation of relativistic mechanics, symplectic approach to canonical transformation, Poisson brackets and other canonical invariants, Liouville theorem, the Hamilton-Jacobi equation, Hamilton’s characteristic function, action-angle variables, integrable systems, transition from a discrete to continuous system, relativistic field theory, Noether’s theorem, Lie groups and group actions, Poisson manifolds, Hamiltonian vector fields, properties of the Hamiltonian fields, conservative chaos, the Poincare surface of section, KAM theorem, Poincare-Birkhoff theorem, Lyapunov exponents, global chaos, effects of double dissipation and fractals.

PC5212 Physics of Nanostructures

The module provides an introduction to the scientific foundations of the function, fabrication and characterization of nano-structured materials and nano-devices. The topics covered are: reviews of quantum mechanics in reduced dimensions and solid state physics, common techniques for nano-structure fabrication and characterization, transport in low-D systems, optoelectronics of nanostructures, nanotubes and nanowires, clusters and nano-crystallites, molecular electronics, magnetic nano-structures. This module is designed for postgraduate students who are interested in nanoscience and nanotechnology research and applications.

PC5213 Advanced Biophysics

This module focuses on theories and techniques used in some important areas of biophysics and life sciences. The topics covered are: quantum mechanical approach of light and transition; absorption spectroscopy; linear and circular dichroism of biological molecules; emission spectroscopy, fluorescence spectroscopy and applications to biomacromolecules; NMR; equilibria of macromolecular solutions; biomembrane structure and transport of macromolecules and transport across biomembranes; kinetics and techniques of protein crystallization; biomineralization/demineralization in human body. This module also includes a lab component. This module is targeted at both physics and non-physics students who already have a basic knowledge in physics, thermodynamics and molecular biology.

PC5214 Essential Techniques in Experimental Physics

The ability to setup high-quality experiments and measurements is fundamental to innovation in many areas of sciences and engineering, including materials and devices. Therefore a good understanding of, and practical training, in experimental physics techniques is essential to a lot of research and development work in both academia and industry. This course equips students with the essential knowledge and practical skills in a broad range of modern experimental physics techniques, including: mechanical design and materials selection; vacuum technology, cyostats, and thin-film deposition techniques; Gaussian beam laser optics; photodetectors; stepper motors and piezoelectric actuators; feedback and control loops; techniques in analog, digital and pulse signal processing; weak-signal detection and lock-in amplifiers; fast-signal detection and transmission lines. The practical skills will be taught in laboratory classes, which are part of this course.

PC5215 Numerical Recipes with Applications

Covers computational techniques for the solution of problems arising in physics and engineering, with an emphasis on molecular simulation and modelling. Topics will be from the text, “Numerical Recipes”, Press et al, supplemented with examples in materials and condensed matter physics. This course insures that graduate students intending to do research in computational physics will have sufficient background in computational methods and programming experience.

PC5228 Quantum Information and Computation

The module will provide an introduction to the physics and mathematics of quantum information in general and quantum computation in particular. In addition to physics majors, the course addresses students with a good background in discrete mathematics or computer science.The following topics will be covered: (1) Introduction: a brief review of basic notions of information science (Shannon entropy, channel capacity) and of basic quantum kinematics with emphasis on the description of multi-qubit systems and their discrete dynamics. (2) Quantum information: Entanglement and its numerical measures, separability of multi-partite states, quantum channels, standard protocols for quantum cryptography and entanglement purification, physical implementations. And (3) Quantum computation: single-qubit gates, two-qubit gates and their physical realization in optical networks, ion traps, quantum dots, Universality theorem, quantum networks and their design, simple quantum algorithms (Jozsa-Deutsch decision algorithm, Grover search algorithm, Shor factorization algorithm).

PC5239B Special Problems in Physics: Variational techniques

This module will present a unified look at the basic branches of physics (classical mechanics, quantum mechanics, electrodynamics, thermodynamics and statistical physics) from the perspective of variational principles, which offer compact statements of the fundamental laws and are also an important tool for designing models and finding approximate solutions.

PC5251 Applied Machine Learning and Data Science

This module exposes graduate students to examples of Machine Learning and Data Science that are commonly encountered in data analyses in the Physical Sciences (e.g. optics, statistical physics, condensed matter, biological physics). We will take a hands-on approach to implementing, training, and evaluating machine learning models. This module will be taught in the Python programming language. Prior experience in any programming language will be helpful.

PC5252 Bayesian Statistics and Machine Learning

In the age of big scientific data, Bayesian statistical methods and machine-learning techniques are becoming a vital part of the modern scientist’s toolkit. This module provides a graduate-level introduction to the two related fields, with equal emphasis on both. Key topics for the first part include: fundamentals of probability and inference, hierarchical modelling, model validation and comparison, and Monte Carlo methods; for the second part, they include: classification and regression, kernel methods, variational methods, and neural networks. The module will be largely theoretically oriented, with the occasional computational component.

PC5253 Complex Systems Analysis and Modelling

Much of our real world data are manifestations or measurements of their underlying complex interactions. Hence, modelling and analysis of the underlying complex systems can reveal understandings and predictions that complement black-box machine learning tools. This module will cover the basic concepts and tools in analysing complex systems and simulation models, and more importantly why and when we need such white-box tools derived from statistical physics. Certain key concepts in complexity science will be intrudcued. It will also provide hands-on experience with system analysis and imulation modelling in Python.

QT5198 Graduate Seminar in Quantum Information

The graduate seminar module will introduce current topics in quantum information science with an emphasis on recent research results. A balanced discussion of both theoretical and experimental topics will provide an opportunity to discuss in detail the main techniques and overall trends in the broad field of quantum information.

QT5201S Quantum Electronics

In this module, basic electronic techniques related to quantum technologies are introduced at a level that allows students to analyze, design, build and modify electronics encountered in experimental work on quantum technologies. It covers basic circuit design, with a focus on techniques related to typical signal conditioning and processing tasks encountered in experiments and application engineering involving quantum systems like single photon detection and generation, atom and ion traps, laser spectroscopy, optical modulators and some radio-frequency techniques to drive atomic transitions, and electronic techniques at cryogenic temperatures.

QT5201V Complementarity and wave-particle duality

The course will familiarize the students with Bohr’s Principle of Complementarity (with a precise technical meaning) and with the quantitative aspects of Einstein’s wave-particle duality, arguably the most important consequence of complementarity. Thereby, the students will acquire a solid understanding of the basic tenets of quantum theory.