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Coursework
Programmes
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| Physics IVH Course List 2004 |
PHYSICS HONOURS COURSES PHYS6041 Advanced Quantum Theory 2U,( 4C) Pre: PHYS3040 P: Comp: C: Inc: Coordinator: Professor Gerard J. Milburn Assessment:40% assignment and 60% end of semester examination. Description: This course introduces non-relativistic many body theory and relativistic quantum field theory. Quantum many body theory is the foundation of much of modern condensed matter physics. We will cover both bosonic and fermionic systems with particular applications in condensed mater physics such as BCS superconductivity, quantum Hall effect, and atomic Bose-Einstein condensation. In relativistic quantum field theory we treat elementary quantum electrodynamics, introducing Feynman diagrams, with applications including Compton scattering and the Lamb shift. Core Content: 1.Many-body quantum physics ("second quantization") 1.1.Quantum descriptions of multi-particle systems 1.2.Field operators 1.3.Second quantised formalism 1.4.Noninteracting mulitparticle systems 1.5.Mulitparticle systems with binary interactions 2.Applications of many-body quantum physics 2.1. Bose-Einstein condensation (BEC) 2.2.Mean-field theory 2.3.Bogoliubov theory 2.4 BCS theory 3.Elements of quantum field theory 3.1.Classical and quantum particle dynamics (review) 3.2.Classical and quantum field theory 3.3.Symmetries in field theory 4.Relativistic scalar field 4.1.Klein-Gordon wave equation 4.2.Quantised Klein-Gordon field 4.3.Covariant commutators 5.Relativistic spinor field 5.1.Spinors 5.2.Lorentz group 5.3.Dirac wave equation 5.4.Quantised Dirac field 6.Electromagnetic field. 6.1.Maxwell equations 6.2.Lorentz Gauge 6.3.Quantised EM field 7. Quantum electrodynamics (QED) 7.1 EM+Dirac field interaction 7.2 Scattering theory 7.3 Elementary Feynman diagrams 7.4 Rutherford scattering 7.5 Compton scattering 7.6 Lamb Shift |
PHYS6050 Advanced Electromagnetic Theory 2U (4C) Pre:PHYS3050 P: Comp: C: Inc: Coordinator: Dr Timo Nieminen Assessment:50% assignment and 50% end of semester examination Description: This course consists of a survey of advanced electromagnetic theory, with detailed coverage of some important applications. Topics cover the mathematical structure of electromagnetic theory, including the mathematical basis of computational electromagnetics, radiation and scattering, photonics, and relativistic electrodynamics. Students will gain a sound understanding of the theory of electromagnetism and topics relevant to research and practical application. 13. Core Content: 1. Mathematics of field theory 1.1 Review of vector and tensor analysis 1.2 Coordinate systems 1.3 Operators 1.4 Orthogonal functions 1.5 Partial differential equations 2. The Maxwell equations 2.1 Historical perspective 2.2 The Maxwell equations, equation of continuity, constitutive relations 2.3 Differential and integral formulations 2.4 Boundary conditions 2.5 Potentials and gauges 2.6 Special cases of the Maxwell equations 2.7 Transport of energy, momentum and angular momentum 3. Steady-state electromagnetics 3.1 Electrostatics 3.2 Magnetostatics 3.3 Time-harmonic fields 4. Propagation of electromagnetic waves 4.1 Electromagnetic waves 4.2 Helmholtz equation and its general solutions 4.3 Multipole expansion 4.4 Common approximations 4.5 Computational electromagnetics 5. Radiation and scattering 5.1 Basic principles and terminology 5.2 Geometrically simple scatterers 5.3 Useful limiting cases 5.4 Multiple scattering 5.5 Periodic structures 5.6 Antennas 5.7 Basis of computational methods 6. Photonics 6.1 Guided waves 6.2 Dielectric waveguides: planar and fibres 6.3 Gratings and photonic crystals 7. A closer look at electromagnetism in material media 7.1 Microscopic Maxwell equations 7.2 Dispersion 7.3 Causality and Kramers-Kronig relations 7.4 Effective medium theories 7.5 Non-linear optics 7.6 Solitons 7.7 Propagation in plasmas 8. Manifestly relativistic electromagnetism 8.1 Maxwell equations 8.2 Lorentz transformations 8.3 Special relativity 8.4 Dynamics of relativistic particles and fields 8.5 Cerenkov radiation 8.6 Lienard-Wiechert potentials |
PHYS4060 Laser Physics and Atom-Light Interaction 2U (4C) Coordinator: Prof. Halina Rubinsztein-Dunlop / A/Prof Norman Heckenberg Assessment: 40% assignmentsand 60% end of semester examination Description: Physics of light-atom interactions including: stimulated and spontaneous emission; coherent effects; laser behaviour and applications; atomic and molecular spectroscopy; nonlinear optics; field propagation in free-space and guiding structures; detectors; semiclassical models of atom-light interactions, including rate equations. Tutorials include demonstration sessions with a range of lasers operating in the department. . Core Content: Physics of light-atom interactions including: stimulated and spontaneous emission; coherent effects; laser behaviour and applications; atomic and molecular spectroscopy; nonlinear optics; field propagation in free-space and guiding structures; detectors; semiclassical models of atom-light interactions, including rate equations. Tutorials include demonstration sessions with a range of lasers operating in the department. |
PHYS4070 Advanced Computational Physics 2U (4C) Pre:PHYS2020 P: PHYS3071 or MATH3203 Comp: C: Inc: Coordinator: Professor Peter D Drummond Assessment: 50% projects and 50% end of semester examination. Description: This course introduces stochastic and Monte Carlo methods in computational physics. These methods are based on random number generation, and offer a powerful set of tools for treating complex physical systems where exact solutions, even using a computer, are not practicable due to computational complexity. The topics covered include random number generation and statistical reliability, Monte Carlo integration on large-dimensional spaces, direct dynamical simulation with Monte Carlo methods, the Metropolis algorithm for statistical ensembles, and the solution of stochastic differential equations. Core Content: Core Content: 1 Introduction to Monte carlo concepts 2 Pseudo-Random Number Generators 2.1 Definitions 2.2 Uniform Distributions of Random Numbers 2.3 Nonuniform Distributions of Random Numbers 3 Statistical Tests of Random Number Sequences 3.1 The Chi-squared Test 3.2 The Kolmogorov-Smirnov Test 3.3 Tests of Random Numbers 4 Monte Carlo Methods 4.1 Monte Carlo Integration 4.2 Importance sampling 4.3 Direct Simulation Monte Carlo: evolution to thermal equilibrium 5 Markov Chain Monte Carlo (MCMC) 5.1 Markov Processes and Chains 5.2 Random Walks and Brownian Motion 5.3 Metropolis Algorithm 5.4 Ising Model: critical point phase transitions 6 Stochastic Differential Equations 6.1 Stochastic methods 6.2 Ordinary stochastic differential equations: Brownian motion 6.3 Partial Stochastic Differential Equations 6.4 Fourier Transform Methods 6.5 Numerical Errors |
PHYS 4090 Quantum Optics and Stochastic Processes 2U (4C) Pre: PHYS3020+3040+3050 P: Comp: C: Inc: Coordinator: Dr. Zbigniew Ficek and Dr. Howard Wiseman Assessment: 40% assignment and 60% end of semester examination Description: The course covers the background theory of various effects discussed from first principles, and as clearly as possible, to introduce students to the main ideas of quantum optics and stochastic processes and to teach the mathematical methods and techniques used by researches working in the fields of quantum and atom optics. Some of the key problems of quantum optics and stochastic processes are also described, concentrating on the techniques, results and interpretations. No attempt has been made at a complete exploration of all the problems of quantum and atom optics, but it is hoped that the problems explored here will provide a useful starting point for those interested in learning more. The intention is to select problems which are not necessarily the most recent or advanced, but which have been most influential on the directions of research in quantum and atom optics. The goal to which this course aspires is a compact logical exposition of the fundamentals of quantum optics and stochastic processes and the applications to atomic and quantum physics, to study quantum properties of matter and radiation. Core Content: Quantum Optics 1. Quantization of the Free EM Field Maxwell's equations for the EM field Wave equation Hamiltonian of the EM wave Quantization 2. Hamiltonians for Quantum Optics Interaction Hamiltonian Hamiltonian of an atomic system 3. Detection of the EM Field and Correlation Functions Semiclassical theory of photodetection Quantum theory of photodetection 4. Interaction-Free Measurements Negative-result measurement Schemes of interaction-free measurements 5. Representations of the EM Field Detection of the EM field and correlation functions Fock states representation Field in a photon number state Probability distributions of photons Coherent states of the EM field Displacement operator Expansions in terms of coherent states 6. Photon Phase Operator Exponential phase operator Susskind-Glogower phase operator Pegg-Barnett phase operator 7. Squeezed States of Light Definition of squeezed states of light Squeezed coherent states Multimode squeezed states Squeezed states of atomic spin variables Spin squeezing Detection of the squeezed states 8. Phase Space Representations of the Density Operator Density operator Number state representation Coherent States P representation Generalized P representations Q representation Wigner representation Relations between the Wigner, Q and P representations Phase space description 9. Single Mode Interaction The Jaynes-Cummings model Collapses and revivals 10. Multimode Interaction Master equation Spontaneous emission and decoherence Effect of the counter-rotating terms on spontaneous emission Heisenberg equations of motion Langevin equations Lorenz-Maxwell equations Floquet method Dressed atom model: Atom-field entangled states 11. Fokker-Planck Equation Photon number representation P-representation Drift and diffusion coefficients Solution of the Fokker-Planck equation Stochastic differential equations (SDE) 12. Classical and Quantum Interference First-order coherence and Welcher Weg problem Second-order coherences Two-photon non-classical interference and quantum nonlocality 13. Atom-Atom Entangled States Entangled states of two identical atoms Entangled states of two nonidentical atoms Two-atom one-photon interference Two-atom two-photon interference 14. Laser Model in the High-Q Limit Stochastic differential equations Semiclassical steady-state solution and stability Exact steady-state solution Laser linewidth 15. Input-Output Theory 16. Motion of Atoms in a Laser Field Diffraction of atoms in a standing laser field Radiation force on atoms Stochastic Processes 1. Historical introduction to stochastic processes. Revision of probability theory. 2. Definition of some important properties of stochastic processes. 3. Markov processes. The Differential Chapman-Kolmogorov equation. 4. Classical master equations and the Fokker-Planck equation. 5. Stochastic Differential Equations (SDEs). 6. The Ito and Stratonovich calculi, and their physical interpretation. Solvable examples. 7. Quantum Stochastic Processes. Revision of quantum probability theory. 8. Generalised measurements in quantum mechanics. 9. The Quantum Master Equation, derivation and examples. 10. Quantum trajectories: jumps and diffusion. |
MATH4105 General Relativity Prerequisite subjects: (i) Compulsory: (PH244 or PHYSxxxx)
+ (MATH3102 or PH348 or PHYSxxxx)
Incompatible subjects: ID435 Subject description Manifolds, tensors, connections & covariant differentiation, parallel transport , geodesics & curvature, differential forms. Foundations of general relativity. Applications to astronomy & cosmology. Nature of assessment: Examinations: Final examination 70% Assignments Introduction to the foundations of the general theory of relativity. Applications of the theory in astronomy & cosmology. Skills: Advanced modelling skills in differential geometry & general relativity. Ability to apply at the research interface. Perspectives: Understanding the power of geometric reasoning in advanced modelling. Appreciation Weekly/fortnightly problem-solving assignments worth 30%. Core content: The concept of an n-dimensional Riemannian or pseudo-Riemannian manifold; properties of covariant & contravariant tensors & tensor fields; connections & the idea of absolute (covariant) derivatives of tensor (fields); notion of parallel transport of vectors & tensors along a curve; definition of the equation of geodesics; null geodesics; curvature tensor; Bianchi identities; Einstein & Weyl tensors; Laplace-Beltrami operator & covariant notions of div & curl; differential forms; fibre-bundles & related geometric structures. of the key ideas of general relativity and its implications for astronomy & cosmology. |
PHYS4030 Condensed Matter Physics (first offered 2005) 2U (4C) Pre: PHYS3020 + 3040 P: Comp: C: Inc: PHY3030 or 6030 Coordinator: Ross McKenzie Assessment: Assignments (30%) and end of semester exam (70%). Description: It will be shown how the electronic properties of crystals can be understood in terms of quantum mechanics and statistical mechanics. What distinguishes metals, 4072semiconductors, and insulators? The course will be useful to students in physics, chemistry, and materials and electrical engineering. . Core Content: Electronic properties of crystals. The Drude and Sommerfeld models. Electrons in a periodic potential. The Bloch model. Metals versus Insulators. Transport theory. Magnetism. Superconductivity. Semiconductors. Electronics on the nano-scale. The Quantum Hall effect. |
PHYS 4072 Experimental Techniques (first offered 2005) 2U (4C) Pre: PHYS2810 and (2041 or 2090)P: Comp: C:PHYS3071 and (3810 or 3820) Inc: Coordinator: Dr Andrew White & Dr Gary Tuck Assessment: 50% assignments and 50%end of semester examination Description: Techniques of experimental design and data analysis for physics. Statistical techniques and their application to data (including errors and sampling). Transform analysis of linear systems (e.g. Fourier and wavelet) and key applications. Aspects of experimental technologies: design of mechanical systems; properties of special materials; vacuum technique; detection of radiation. One or more case studies of experimental design. These techniques are broad in application, and transferable to any field utilising sophisticated measurement technology , e.g. astronomy, biophysics or engineering. Core Content: Signals in linear systems. Continuous vs discrete systems. Transform methods and applications. Data fitting techniques. Factors in instrument design (mechanical and electrical). Noise. Vacuum technology. Material properties. Case studies. |
MATH4108? Algebraic Methods in Mathematical Physics (first offered 2005) DRAFT ONLY #2 (3C)Semester 2 Pre: MATH3401 Comp: MATH3102 Coordinator: Professor Mark Gould Assessment: Assignments + Examination Description: Algebraic structures & their representations of importance to current mathematical physics research: Lie algebras & superalgebras; quantum groups & algebras; Hopf & quasi-Hopf algebras; affine and Kac-Moody algebras. Illustrative applications to knot theory & physics. Offered in odd-numbered years. |
MATH4104 Hamiltonian Dynamics and Chaos . Prerequisite subjects: (i) Compulsory: PH244 or PHYSxxxx (ii) Recommended (not compulsory): MATH3101 Incompatible subjects: ID436 Subject description Lagrangian & Hamiltonian dynamics: differential & symplectic manifolds, differential forms, canonical transformations, Hamilton-Jacobi methods. Perturbation theory, integrable systems, KAM theorem, area-preserving maps, Poincare-Birkhoff theorem, criteria for chaos, ergodicity, mixing. Offered in odd numbered years only. Nature of assessment: Examinations: Final examination 70% Assignments :Weekly/fortnightly problem-solving assignments worth 30%. Core content Core content: Concepts of advanced Hamiltonian dynamics & chaos. Skills: Advanced problem-solving skills in Hamiltonian dynamics, in particular those appropriate for the analysis of integrable and chaotic systems. Perspectives: Understanding use of advanced mathematics and physics in understanding Hamiltonian dynamics & chaos. |
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Department
of Physics, The University of Queensland |
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