Code  Title  MC  Sem I  Sem II 

Graduate Seminar Module in Physics  4 
 
Thomas OSIPOWICZ & WANG Xuesen 

Advanced Quantum Mechanics  4 
OH Choo Hiap 
 

Advanced Statistical Mechanics  4 
 
WANG JianSheng 

Advanced Solid State Physics  4 
 
Benoit GREMAUD 

Special Topics in Physics  4 
Ramanathan MAHENDIRAN 
 

Topics in physics: Analytic Approximations  4 
 
WANG Qinghai 

Topics in Surface Physics  4 
 
 

Selected Topics in Quantum Field Theory  4 
WANG Qinghai 
 

Topics in Optical Physics  4 
LING Euk Jin Alexander 
 

Superconductivity  4 
 
 

Accelerator Based Materials Characterisation  4 
CHAN Taw Kuei 
 

Advanced Dynamics  4 
 
GONG Jiangbin 

Physics of Nanostructures  4 
 
WANG Xuesen 

Advanced Biophysics  4 
 
YAN Jie & Artem EFREMOV 

Principles of Experimental Physics  4 
 
 

Numerical Recipes with Applications  4 
WANG JianSheng 
 

Advanced Atomic and Molecular Physics  4 
 
 

Quantum Information and Computation  4 
Dzmitry MATSUKEVICH 
 

Special Problems in Physics: Quantum gases – interactions and statistics  4 
 
 

Photonics II  4 
 
LI Wenhui 

M.Sc Coursework Thesis for Physics  12 
project based 
project based 

M.Sc Coursework Thesis for Applied Physics  16 
project based 
project based 

Quantum Measurements and Statistics  4 
Dagomir KASZLIKOWSKI 
 

Graduate Seminar in Quantum Information  4 
 
Valerio SCARANI 

Convex Optimization and Quantum Foundations  4 
Valerio SCARANI/CAI Yu/Antonios VARVITSIOTIS 
 
Brief Description of Modules
Prerequisite & Preclusion(s): please refer to NUS Bulletin Online
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 manybody 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, FokkerPlanck 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.
Click here to visit the course materials/website.
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, electronelectron interaction and HartreeFock 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
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 & biomolecule 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 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 solidstate 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 opticsrelated 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, opticalinduced birefringence, selffocusing, nonlinear optical absorption, photonic devices; ultrafast laser.
PC5208 Superconductivity
The purpose of this course is to provide an introduction to the microscopic and phenomenological theories of superconductivity. It lays the analytical foundation for the understanding a wide range of modern applications of both low and high temperature superconductors. The lecture links established theories with current research activities in the development of the physics and technology of the superconductors. Students should have a background in quantum mechanics and thermal physics.
PC5209 Accelerator Based Materials Characterisation
The course gives an introduction to the physics of ion beam analysis. After a general introduction, interatomic potentials, cross sections and stopping powers are discussed, and the theory of the stopping process is developed based on the ThomasFermi statistical atom. Accelerators and other instrumentation are introduced, and a range of analytical techniques is discussed in detail: Rutherford Backscattering (RBS), Proton Induced Xray 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 HamiltonJacobi equation, Hamilton's characteristic function, actionangle 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, PoincareBirkhoff 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 nanostructured materials and nanodevices. The topics covered are: reviews of quantum mechanics in reduced dimensions and solid state physics, common techniques for nanostructure fabrication and characterization, transport in lowD systems, optoelectronics of nanostructures, nanotubes and nanowires, clusters and nanocrystallites, molecular electronics, magnetic nanostructures. 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 nonphysics students who already have a basic knowledge in physics, thermodynamics and molecular biology.
PC5214 Principles of Experimental Physics
This module provides experimental knowledge on techniques used in modern optical and atomic physics. The focus is on practical implementation of optical measurement methods, and the corresponding technology. Areas covered are practical photodetection, lockin signal recovery, simple feedback systems, FPI cavities, optical thin films, basic vacuum systems, manipulation of cold atoms, and aspects of working at low temperatures (below 77K). The module will have a strong focus in practical techniques, targeting students who intend to work in the area of atomic, molecular, ion and optical or cryogenic physics.
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.
Click here to visit the course materials/website.
PC5216 Advanced Atomic and Molecular Physics
This module introduces from an experimentalists point of view to the modern world of ultracold quantum gases that so much changed atomic physics in the past two decades. The lectures present the basic experimental methods of laser cooling, magnetic and optical trapping, and evaporative cooling that produce matter near absolute zero temperature. We then discuss basic effects like BoseEinstein condensation and Pauli pressure. Further, selected research examples are presented that give insight to some of the many close relations between quantum matter designed in many labs worldwide and other physical systems found in the range of quantum information science, condensed matter physics, metrology, nuclear physics, and astronomy. Solid background in quantum mechanics, atomic physics, and statistical mechanics is desired.
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 multiqubit systems and their discrete dynamics. (2) Quantum information: Entanglement and its numerical measures, separability of multipartite states, quantum channels, standard protocols for quantum cryptography and entanglement purification, physical implementations. And (3) Quantum computation: singlequbit gates, twoqubit gates and their physical realization in optical networks, ion traps, quantum dots, Universality theorem, quantum networks and their design, simple quantum algorithms (JozsaDeutsch decision algorithm, Grover search algorithm, Shor factorization algorithm).
PC5239 Special Problems in Physics: Quantum gases – interactions and statistics
This creditable, oneoff course is offered by visiting prof. Jook Walraven, University of Amsterdam. The lectures introduce basic concepts of the physics of ultracold quantum gases  lowdensity gases of neutral atoms studied at (sub)microkelvin temperatures. Quantum gases are important both from the fundamental point of view and for their potential application in quantum information processing. The course is focused on quantum collisions and quantum statistics as these phenomena provide the underpinning for the very existence of the field. A systematic introduction is given into the quantum mechanics of lowenergy collisions and the consequences of the quantum statistical nature of the collision partners for the behaviour of the gas. The students will learn to distinguish between varieties of collisional phenomena and understand their consequences both from the kinetic and the thermodynamic point of view. The course is optimized for experimentalists with a theoretical interest. Background in quantum mechanics and statistical mechanics is desired.
Keywords: classical versus quantum gas, evaporative cooling, shortrange potentials (range, scattering length, effective range), swave scattering regime, swave resonances, shape resonances, Feshbach resonances, differential and total cross section, RamsauerTownsend minima, scattering of identical particles, interaction energy, chemical potential and mean field.
PC5247 Photonics II
The module is intended to provide detailed treatment of the principles of lasers and working knowledge of major optical techniques used in manipulating laser spatial mode properties and their temporal and spectral characteristics. The topics being covered include laser beams, laser theory, laser survey, modulation techniques, nonlinear optics, and fiber optics.
QT5101 Quantum Measurements and Statistics
This module deals with quantum measurement theory and the interpretation of the observed statistics. It covers notions like decoherence, generalized uncertainty relations and Bell's inequalities. Emphasis is put on providing both the understanding of the concepts and the ability of using the mathematical tools.
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.
QT5201N Convex Optimization and Quantum Foundations
This module will introduce graduate students in NUS to the use of techniques from convex optimization to study the foundations of quantum mechanics. The module will provide an unique opportunity to learn advanced techniques from active researchers in the field of interest. Students will learn basics notions from convex analysis (faces, extreme points, exposed points) and convex optimization (linear optimization, semidefinite optimization) and how these are used to solve problems in the foundations of quantum mechanics. Concepts as well as concrete applications at the research frontier are presented. The implementation of this module introduces students to a new and exciting area of research at an advanced technical level. This selective training provides an excellent opportunity to hone research skills. There is no similar module offered by NUS. This module is open to all students in CQT, and those in Computer Science, Mathematics, and in Physics. Students from other departments and faculties are welcome, but it is advisable that they discuss their background with one of the lecturers before registering.