If you are looking at a printed version of this document, please refer to
http://www.maths.uq.edu.au/courses/MATH4104/index.html
for up-to-date information

The first half will be given by Dr Cathy Holmes. You can contact me, or obtain information:

• in person: Priestley building (Mathematics), Room 69-708. My set contact times are Monday 11am-12noon, Tuesday, 1-2pm and Thursday 1-2pm, but am happy to see you at other times, pref Tue, Thursday and Friday.
• via phone: 3365 3262 (my office), or 3365 3277 (departmental secretaries)
• via email: cah@maths.uq.edu.au
• from this course's home page: http://www.maths.uq.edu.au/courses/MATH4104/index.html

The second half will be given by Prof Gerard Milburn.

• Information for this half can be obtained at http://homepage.mac.com/gmilburn/index.html or go to Gerard Milburn's home page.

Please do not hesitate to contact us if you have any difficulties or questions.

Lectures and Tutorials

MATH4104 is worth 2 units.

There are three hours of lectures per week and one tutorial.

Lectures

• Monday 10am Room 67-641
• Wednesdaxy 9am, room Physics annex Rm 6- 407
• Fri 11am-12noon, room 67-641

  Tutorial Tuesday 10am or Thursday at 11am 67-641

• Note There are NO tutorials in the first week!

  Tute Sheets (PDF Files)

  Tute Sheet 1 Solutions to Tute Sheet 1

  Tute Sheet 2 Solutions to Tute Sheet 2

  Tute Sheet 3 Solutions to Tute Sheet 3

  Note Quantum Mechanics Assignment 1 is due 25th of September and not 18th.

  Quantum Mechanics Assignment 1

  Quantum Mechanics Assignment 2

  10% assignment(Classical)

  10% assignment (Quantum)

  Assessment

  Assessment will consist of

  Part 1 (Classical Dynamics ). Three tutorial assignments worth in total 10% and a project type assignment worth 10%,

  Part 2 (Quantum Dynamics). Three tutorial assignments worth in total 10% and a project type assignment worth 10%,

  a final exam ( on all of the course) worth 60%.

  Past Exam (PDF Files)

  Solutions to first half of 2007 Exam

  2005 Exam Solutions to first half of 2005 Exam

  Solutions to second half of 2005 Exam

  2003 Exam Solutions to first half of 2003 Exam

  Students should be familiar with the rules which relate to assessment in their degrees as well as general university policy such as found in the General Award Rules. These are all set out on the Program and Course Information page on the UQ website http://www.uq.edu.au/student/courses/.

  Textbooks and Teaching Materials

  Lecture Notes for Classical Hamiltonian Dynamics(PDF Files)

  Lagrangian Mechanics

  Hamiltonian Mechanics

  Canonical Transformations

  Integrability and Action Angle variables

  Canonical Perturbation Theory

  The KAM THeorem

  Twist Maps

  The Standard Map

  Chaos near Homoclinic orbits

  Billiards

  Lecture Notes for Quantum Hamiltonian Dynamics(PDF Files)

  Quantum Chaos

  Lecture 2

  Lecture 3

  Lecture 4

  Lecture 5

  Lecture 6

  Lecture 7

  Lecture 8

  Lecture 9

  Lecture 10

  Lecture 11

  Lecture 12

  random-matrices

  floquet-example

  Dynamical-localisation

  Article on Quantum Chaos by Douglas Stone

  Quantum Notes from PHIL2011

  REFERENCE BOOKS

  Random and Stochastic Motion, A.J. Lichtenberg and M.A. Lieberman, Applied mathematical Sciences vol38, Springer Verlag, New York, 1982.

  The Transition to Chaos, in conservative classical systems: quantum manifestations. Linder Reichl, Springer Verlag, New York, 1992.

  Introduction to Applied Nonlinear Dynamical Systems and Chaos, S. Wiggins, Springer, New York, 1990.

  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of vector Fields, J. Guckenheimer and P. Holmes, Applied Mathematical Sciences vol 42, Springer Verlag, New York, 1983.

  Chaos, an introduction to Dynamical Systems, K.T. Alligood, T.D. Sauer, J.A. York, Springer, 1996.

  Structure and Interpretation of Classical Mechanics, G.J. Sussman, J.Wisdom, MIT Press 2001, www-swiss.ai.mit.edu/~gjs/6946/sicm.html/book.html

  Quantum Signatures of Chaos, F. Haake, Springer Verlag, New York, 1991.

  Quantum chaos : an introduction, Hans-Jurgen Stockmann, Cambridge UP.

  Quantum chaos : between order and disorder :a selection of papers compiled and introduced by Giulio Casati, Boris Chirikov.

  A modern approach to quantum mechanics, Townsend, Mcgraw-Hill (this is the level of QM assumed)

  Course Outline

  Course Outline

  1. Classical Dynamics

  1.1 Lagrangian Mechanics

  1.2 Hamiltonian Mechanics

  1.3 Canonical Transformations

  1.4 Integrability and Action Angle variables

  1.5 Canonical Perturbation Theory

  1.6 Resonances and the KAM theorem

  1.7 Twist Maps

  1.8 The Standard Map

  1.9 Chaos near Homoclinic Orbits

  1.10 Chaos in Billiards

  2. Quantum Dynamics

  2.1 Review of Quantum Theory

  2.2 Atoms in Optical potentials

  2.3 Integrable Non-linear Quantum Dynamics

  2.4 Quasi-Integrable Non-linear Quantum Dynamics

  2.5 Dynamical Localisation

  2.6 Non-Linear Quantum Maps

  2.7 Random matrices

  2.8 Trace Formulae and Periodic orbits

  2.9 Quantum Billiards

  2.10 Mesoscopic Systems

  Assessment dates

  The due dates for each of the items of assessment are as follows.

  • Tute 1 : due Friday 14th August by 5pm.
  • Tute 2 due Friday 28th August by 5pm.
  • Tute 3: due Friday 11th September by 5pm.
  • Tute 4: due Friday 25th September by 5pm.
  • Tute 5: due Friday 16TH October by 5pm.
  • Tute 6: due Friday 30TH October by 5pm.
  • 10% Project Assignment 1 : due Friday 30th October
  • 10% Project Assignment 2 : due Friday 30th October

  Grade Criteria

  To earn a Grade of 7, a student must demonstrate an excellent understanding of the course material. This includes clear expression of nearly all their deductions and explanations, the use of appropriate and efficient mathematical techniques and accurate answers to nearly all questions and tasks with appropriate justification. They will be able to apply mathematical techniques to completely solve both theoretical and practical problems.

  To earn a Grade of 6, a student must demonstrate a comprehensive understanding of the course material. This includes clear expression of most of their deductions and explanations, the general use of appropriate and efficient mathematical techniques and accurate answers to most questions and tasks with appropriate justification. They will be able to apply mathematical techniques to partially solve both theoretical and practical problems.

  To earn a Grade of 5, a student must demonstrate an adequate understanding of the course material. This includes clear expression of some of their dedu ctions and explanations, the use of appropriate and efficient mathematical techniques in some situations and accurate answers to some questions and tasks with appropriate justification. They will be able to apply mathematical techniques to solve fundamental problems.

  To earn a Grade of 4, a student must demonstrate an understanding of the basic concepts in the course material. This includes occasionally expressing their deductions and explanations clearly, the occasional use of appropriate and efficient mathematical techniques and accurate answers to a few questions and tasks with appropriate justification. They will have demonstrated knowledge of techniques used to solve problems and applied this knowledge in some cases.

  To earn a Grade of 3, a student must demonstrate some knowledge of the basic concepts in the course material. This includes occasional expression of their deductions and explanations, the use of a few appropriate and efficient mathematical techniques and attempts to answer a few questions and tasks accurately and with appropriate justification. They will have demonstrated knowledge of techniques used to solve problems.

  To earn a Grade of 2, a student must demonstrate some knowledge of the basic concepts in the course material. This includes attempts at expressing their deductions and explanations and attempts to answer a few questions accurately.

  A student will earn a Grade of 1 if they show a poor knowledge of the basic concepts in the course material. This includes attempts at answering some questions but showing an extremely poor understanding of the key concepts.

  Graduate Attributes

  1. In-Depth Knowledge of the Field of Study

     • You will get an in-depth understanding of the mathematical techniques required to understand Classical and Quantum Hamiltonian systems through attending lectures and solving the assignment problems and undertaking projects.
     • You will obtain an understanding of the applications of Hamiltonian Dynamics to other fields through applying techniques to systems from biology, physics and chemistry.
     • By completing the project you will receive an understanding of computational applications of mathematics as applied to this area.

  2. Effective Communication

     • You will gain the ability to present a logical sequence of reasoning using appropriate mathematical notation and language.
     • You will get the ability to select and use the appropriate level, style and means of written communication, using the symbolic, graphical, and diagrammatic forms relevant to the context.

  3. Independence and Creativity

     • You will improve your ability to work and learn independently.
     • You will get the ability to generate and synthesise ideas and adapt innovatively to changing environments.
     • You will obtain the ability to formulate problems mathematically.
     • You will receive the ability to generate approaches for the mathematical solution of problems including the identification and adaptation of existing methods.
     • You will receive skills to effectively and appropriately use computing technologies.

  4. Critical Judgement

     • You will improve your ability to identify and define problems.
     • The ability to evaluate methodologies and models, to make decisions and to reflect critically on the mathematical bases for these decisions.
     • The ability to apply critical reasoning to analyse and evaluate a piece of mathematics.

  5. Ethical and Social Understanding

     • Students will obtain knowledge and respect of ethical standards in relation to working in the area of mathematics.
     • You will get an appreciation of the history of mathematics as an ongoing human endeavour.

  General comments

  The University expects that most students will need to spend about 12 hours per week on this course, including class contact. A few people may need to take a bit longer, while some might manage with a little less time each week; it will depend upon your mathematical background. You are welcome to attend additional tutorials if you feel it will help.

  Supplementary examinations:

  In some programs, a supplementary examination may be awarded in one course to students who obtain a grade of 2 or 3 in the final semester of their program and require this course to finish their degree. You should check the rules for your degree program for information on the possible award of supplementary examinations. Applications for supplementary examinations must be made to the Director of Studies in the Faculty.

  Special examinations:

  If a student is unable to sit a scheduled examination for medical or other adverse reasons, she/he can and should apply for a special examination. Applications made on medical grounds should be accompanied by a medical certificate; those on other grounds must be supported by a personal declaration stating the facts on which the application relies.

  Applications for special examinations for central and end-of-semester exams must be made through the Student Centre. Applications for special examinations in school exams are made to the course coordinator.

  More information on the University's assessment policy may be found http://www.uq.edu.au/hupp/contents/view.asp?s1=3&s2=30&s3=5

  Feedback on assessment:

  You may request feedback on assessment in this course progressively throughout the semester from the course coordinator. Feedback on assessment may include discussion, written comments on work, model answers, lists of common mistakes and the like.

  Students may peruse examinations scripts and obtain feedback on performance in a final examination provided that the request is made within six months of the release of final course results. After a period of six months following the release of results, examination scripts may be destroyed.

  Information on the University's policy on access to feedback on assessment may be found at http://www.uq.edu.au/hupp/contents/view.asp?s1=3&s2=30&s3=5

  Students with disabilities or special needs:

  Any student with a disability who may require alternative academic arrangements in the course is encouraged to seek advice at the commencement of the semester from a Disability Adviser at Student Support Services. If you have any special needs or requirements with which I can help, please do not hesitate to contact me.

  Assistance for Students:

  Students with English language difficulties should contact the course coordinator or tutors for the course. Students with English language difficulties who require development of their English skills should contact the Institute for Continuing and TESOL Education on extension 56565.

  The Learning Assistance Unit located in the Relaxation Block in Student Support Services. You may consult learning advisers in the unit to provide assistance with study skills, writing assignments and the like. Individual sessions are available. Student Support Services also offers workshops to assist students. For more information, phone 51704.

  Student Liaison Officer:

  The School of Physical Sciences has a Student Liaison Officer as an independent source of advice to assist students with resolving academic difficulties.

  The Student Liaison officer during 2005 will be Assoc Prof Peter Adams, Room 547 Priestley building, (email pa@maths.uq.edu.au)

  Assumed background / prerequisites

  Some previous knowledge with ODE's is assumed. In particular solving linear constant coeffcient ODE's and nonlinear first order ODE's via the method of separation of variables. Students should also be familiar with linear systems of ODE's, fundamental matrices and phase plane analysis for linear 2D systems with constant coefficients, although this last topic is reviewed.

  ---

  Cathy Holmes
  

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