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Transcript
University of Cape Town
Department of Physics
— Honours booklet 2016 —
Department of Physics
University of Cape Town
Private Bag X3
Rondebosch 7700 · South Africa
www.phy.uct.ac.za/phy/courses/PHY4000W
Contents
1 General information
1.1 Structure of the course . . . . . . . .
1.2 Admission criteria . . . . . . . . . .
1.3 Standard of the course and workload
1.4 Module choice . . . . . . . . . . . . .
1.5 Research project . . . . . . . . . . .
1.6 Duly performed (DP) certificate . . .
1.7 Examinations . . . . . . . . . . . . .
1.8 Aggregation of marks . . . . . . . .
1.9 Facilities . . . . . . . . . . . . . . . .
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2 Description of Modules
2.1 Compulsory and Physics-elective Modules . .
2.1.1 Classical Mechanics (CM) . . . . . . .
2.1.2 Computational Physics (CP) . . . . .
2.1.3 Electrodynamics 1 (ED1 ) . . . . . . .
2.1.4 Electrodynamics 2 (ED2 ) . . . . . . .
2.1.5 Kick-off module (KO) . . . . . . . . .
2.1.6 Nuclear Physics (NP) . . . . . . . . .
2.1.7 Physics Education (PE) . . . . . . . .
2.1.8 Particle Physics (PP) . . . . . . . . .
2.1.9 Quantum Field Theory (QF) . . . . .
2.1.10 Quantum Mechanics 1 (QM1 ) . . . . .
2.1.11 Quantum Mechanics 2 (QM2 ) . . . . .
2.1.12 Relativistic Quantum Mechanics (RQ)
2.1.13 Statistical Physics (SP) . . . . . . . .
2.1.14 Solid State Physics (SS) . . . . . . . .
2.2 Additional Modules . . . . . . . . . . . . . .
2.3 Research Projects . . . . . . . . . . . . . . . .
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iii
Contents
3 Lecture time table
iv
31
1 General information
The Department of Physics at the University of Cape Town (UCT) offers a
one-year BSc Honours degree course with the course code
PHY4000W: BSc (HONS) in PHYSICS.
This course is usually taken by a student in the fourth year of university study,
after having graduated with a BSc in Physics. The BSc Honours degree is the
gateway towards further postgraduate degrees in Physics, such as the MSc and
PhD degrees.
1.1 Structure of the course
The Physics Honours course consists of a supervised Research Project counting
3 units, and 9, 10 or 11 lecture modules, each worth 1 unit. These lecture modules have 20 lectures (45 minutes long), reading assignments, tutorial sessions
and/or problem sets, or equivalent. The modules are categorized as:
• Compulsory Physics modules (8 units, including the Research Project)
• Physics Elective modules (choose at least 2 modules)
• Additional modules
The Compulsory modules contribute 8 units, i. e. two third of the minimum
number of 12 units for the Honours course. The course is to be complemented
by at least 2 Physics Elective modules and, in case (to bring the total number of
units up to 12, 13 or 14), an appropriate number of Additional modules offered
by other departments.
The Honours course will kick off in the UCT orientation week, with activities
to refresh mathematics skills, combined with a Mathematica and (V)Python
introduction/recap, and discussions on the nature of physics and physics education. This ‘Kick-off’ module does not count as a unit, but it is compulsory
to meet the DP criteria (see Section 1.6).
1
1 General information
semester
units
Compulsory
Kick-Off module (KO)
Research Project (RP)
Electrodynamics (ED1 + ED2 )
Quantum Mechanics (QM1 + QM2 )
Statistical Physics (SP)
1
1+2
1
1
2
–
3
2
2
1
Physics Elective
Classical Mechanics (CM)
Computational Physics (CP)
Nuclear Physics (NP)
Particle Physics (PP)
Physics Education (PE)
Quantum field theory (QF)
Solid State Physics (SS)
Relativistic Q-Mechanics (RQ)
1
1
2
2
1+2
2
2
2
1
1
1
1
1
1
1
1
Additional
The modules expected to be offered1 are:
modules
Advanced Math Methods 1+2 [MAM]
General Relativity [MAM]
Programming for Scientists/Engineers [CERECAM]
Continuum Mechanics [CERECAM]
General Astrophysics [AST]
Diagnostic Radiology [Med PHY]
Radiotherapy [Med PHY]
Nuclear Medicine [Med PHY]
...
1+2
1
1
1
1
1
1
2
.
1+1
1
1
1
1
1
1
1
.
Outlines of the Compulsory modules and the Physics Elective modules are given
in Chapter 2; for the time table see Chapter 3.
1
2
The Physics Department reserves the right to delete Physics modules, or add modules, or
modify the list should staffing or other factors so dictate; for updates see the course website
www.phy.uct.ac.za/phy/courses/PHY4000W. Information on the additional modules is
given by the respective departments, see also Section 2.2.
1.2 Admission criteria
1.2 Admission criteria
Admission to the Physics Honours course is at the discretion of the Dean of
Science and the Head of Department of Physics, who will consult the Honours
course convenor. Normally the following criteria are used:
• a pass mark of ≥ 60% in UCT third year Physics courses, or equivalent,
and
• a mathematical background strong enough to ensure success in the course,
which requires a second year UCT Mathematics or Applied Mathematics
course or equivalent. For a Theoretical/Mathematical Physics oriented
choice of modules, a pass mark of ≥ 60% in a third year UCT Mathematics
or Applied Mathematics course, or equivalent, is required.
In exceptional cases a student, who does not meet the above criteria, may be
set reading and study material, and, upon satisfying the Head of Department
that they have mastered this material, may be admitted.
1.3 Standard of the course and workload
The Physics Honours course is intensive. Coming after a three year general BSc
degree, where a student has majored in two, and sometimes only one, subject,
the Honours degree prepares a student for
• beginning a research MSc degree by dissertation
• doing well in the GRE examination for US graduate school
• entry into UK, European or US post-graduate degree, if the student has
done exceptionally well.
The content of the Physics Honours course is similar that of senior undergraduate courses in good UK or US universities.
3
1 General information
A rough estimate of the workload for one typical lecture module is
20 lectures (incl. question time)
reading before and after lecture
5 problem sets/tutorials
independent study
total
20
20
20
20
hours
hours
hours
hours
80 hours
Accordingly, a course of the minimum 12 units would take about 960 hours.
Divided by 120 days (24 weeks in academic term) this equates to 8 hours a day.
The actual workload, including the research project, and including preparation
for examinations, will depend on student preparedness and ability, and may
well be 20 percent higher than this, and will fluctuate throughout the year.
1.4 Module choice
The broad content of a modules is decided between the Head of Department,
who bears ultimate responsibility for the academic content of the course and
its modules, the Honours convenor, and the lecturer concerned.
A student must declare a provisional choice of modules at registration. He
or she can modify this choice by 5pm on the Friday at the end of the first
lecture week. A student can thereafter change the module choice (pickup, drop,
change) only if the Head of Department, after consultation with the Honours
convenor, agrees.
1.5 Research project
Research projects must, in opinion of the Head of Department and after consultation with the Honours convenor, senior colleagues and the project supervisor,
be aligned with the academic nature of the course, e. g. experimental physics,
or theoretical physics, or mathematical physics. The Head of Department will
decide if each proposed research project (title, supervisor, description of nature
of research project) is acceptable.
Available projects are described in Section 2.3.
4
1.6 Duly performed (DP) certificate
A project has to be choosen by each student by end of February. A short
progress report (1/2 – 1 page) is to be submitted one week before last day of
lectures of the first semester. If the Head of Department, after consultation
with the Honours convenor, feels there has not been sufficient progress, a letter
will be sent to the student and the supervisor, warning that the course DP
certificate (see Section 1.6) may be withheld. At the beginning of the second
semester a informal 10’-presentation is to be given on the work done so far.
The final project report, typically 30+ pages,2 is to be submitted by a date
to be set by the Head of Department and the Honours convenor (normally
one week before lectures end); otherwise the DP certificate will be withheld.
This report has a weight of 80% towards the project mark; assessed by the
supervisor, a referee and the Honours convenor are the student’s ability to conduct (supervised) research, including literature review, performing necessary
calculations and/or experimental work, analysis of results as well as their presentation and discussion. Around the report submission date, a 20’ presentation
of the research project is to be given, which will be assessed by the supervisor,
the referee, the Course convenor and the Head of Department and which will
contribute to the project mark with a weight of 20%.
1.6 Duly performed (DP) certificate
Only students who receive a duly performed (DP) certificate, normally issued
one week before the last day of lectures, will be allowed to write the October/November examinations. The DP certificate criteria are:
• a class record of at least 30% for all problem sets and class tests
• convincing progress in the Research Project, in particular the report being
submitted
• attendance of i) the ‘Kick-Off’ module and ii) at least two thirds of the
Departmental colloquia.
1.7 Examinations
Certain modules will be examined in the May/June examination period. Other
modules will be examined in the October/November examination period. Ex2 Theses
from previous years are available in the Physics library.
5
1 General information
ceptionally, by agreement with students and lecturing staff, the Head of Department may direct examinations to take place outside these periods.
A student must declare which modules he or she will sit for examination by
a date to be set by the Head of Department, usually at the beginning of the
3rd last week of lectures.
Results of the examination of all these modules will be used in a final aggregation by the Honours examination committee, a body whose membership
is decided by the Head of Department, but typically will include the Head of
Department, the Honours convenor, lecturers, project supervisors and project
readers as well as the external examiner(s). This Honours examination committee is advisory to the Head of Department, who submits results to the Science
Faculty Examination Committee (FEC) for decision, and ultimate ratification
by the University Senate.
1.8 Aggregation of marks
The final course mark is the mean of the individual module marks, unless the
Head of Department shows good cause, in writing, for deviating from this. In
the average, the research project has a triple weight compared to the lecture
modules (each worth one unit). For a module choice with more than the minimum number of 9 lecture modules, only the 9 best modules are taken into
account (besides the research project).
The pass/fail decision is based on this final mark exceeding the pass mark of
50%, and is further subject to the subminimum criteria of
• obtaining a minimum mark of 50% in the Research Project
• passing two thirds of the chosen lecture modules
• achieving a mark of ≥ 35% in all but two of the Compulsory lecture
modules.
A student who fails the Honours course may not be re-admitted.
6
1.9 Facilities
1.9 Facilities
The Department has a Postgraduate Computer Lab on Level 4 of the RW
James Building which is open to Physics Honours students. The 8 QuadCore+GPU PC’s run both Windows and Linux; available software includes
LATEX, Open/MS Office, Mathematica and V/Python. A printing facility is
available (printing abuse would be detected). Details of Lab and Computer
usage can be found on posters located around the Lab. For further information
contact the Lab administrator Kerwin Ontong, [email protected]
The Honours students have access to the Physics Frahn library on Level
5 of the RW James Building, which provides also quiet working space. Contact
Gregor Leigh, [email protected], for further details.
Last but not least: the Duncan Elliott room on Level 3 of the RW James
Building is a place to meet other Postgrad students and members of staff, to
discuss Physics and more . . . and, of course, to have a cup of tea or coffee after
the third lecture period and/or in the afternoon.
7
2 Description of Modules
2.1 Compulsory and Physics-elective Modules
2.1.1 Classical Mechanics (CM)
Lecturer
20 Lectures
5 Tutorials
Class Test
Exam
A/Prof R. Fearick, [email protected]
First semester
counting 25% towards module mark
counting 25% towards module mark
2 hours, in May/June, counting 50% towards module mark
Outline
Newtonian mechanics: space and time, Newton’s laws, systems with 1 degree of
freedom, central forces, non-inertial frames — Lagrange formalism: the route
to Lagrange’s equations, calculus of variations, Hamilton’s principle of least
action, conserved quantities, transformations of the Lagrangian — Hamilton
formalism: the Hamiltonian, phase space, Poisson brackets, canonical transformations; Advanced methods.
Literature
[1] F. Scheck, Mechanics: From Newton’s laws to deterministic chaos, Springer
2005.
[2] J. V. Jose and E. J. Saletan, Classical Dynamics: A Contemporary Approach, Cambridge 1998.
9
2 Description of Modules
2.1.2 Computational Physics (CP)
Lecturer
20 Lectures
5 Tutorials
Test
Exam
Dr T. Dietel, [email protected]
Second semester
counting 25% towards module mark
Take-home, counting 25% towards module mark
Take-home, in October/November, counting 50% towards
module mark
Students are expected to be familiar with at least one programming language.
Outline
In the real world, very few deterministic problems can be solved analytically.
Furthermore, many physical processes are stochastic. In both cases, physicists
look to computers to shed light on the physics. In this course, several of the
more ubiquitous numerical methods will be introduced that form part of most
physicists’ toolkits. Topics to be presented will be drawn from:
Monte Carlo techniques of sampling, integration and simulation — Numerical calculus (including integration using orthogonal polynomials) — Function
interpolation, extrapolation and fitting (including the technique of Smoothed
Particle Hydrodynamics) — ODE and PDE solution.
Literature
[1] R. de Vries, A first course in computational physics, Wiley 1994.
[2] A. L. Garcia, Numerical methods for physics, Prentice-Hall 1994.
[3] N. J. Giordano, Computational Physics, Prentice-Hall 1997.
[4] T. Pang, An introduction to computational physics, Cambridge 2006.
[5] W. H. Press et al., Numerical recipes, Cambridge (various editions for
different programming languages).
10
2.1 Compulsory and Physics-elective Modules
2.1.3 Electrodynamics 1 (ED1 )
Lecturer
20 lectures
5 tutorials
Class test
Exam
A/Prof H. Weigert, [email protected]
First semester, first quarter
counting 25% towards module mark
counting 25% towards module mark
2 hours, in May/June, counting 50% towards module mark
Electrodynamics is an “old” theory dating back into the formative years of a science
later to be called physics. Yet it is strangely modern: It is in fact fully relativistic
(and was so long before Einstein); it is usually taught before quantum mechanics, yet
many of the tools usually only properly taught in quantum mechanics have essential
uses in electrodynamics (were in fact invented there to be reused and refined to
formulate quantum mechanics) and in particular, it is the precursor of Quantum
Electrodynamics (QED) a key part of our Standard Model of Particle Physics, one
of our deepest microscopic theories of nature. In this honours course, were you, the
students should have at least a smattering of all of these references at your disposal,
I will attempt to build on these connections to help you develop a better sense of the
unity of physics as a science, hopefully breaking a few barriers to scientific thinking
in the process.
Outline
History and perspective – introduction to vector calculus – basic principles
of electrostatics – solving differential equations: Green’s functions, boundary
conditions, complete sets of states – electrostatics in media – magneto-statics
– magneto-statics in media – electrodynamics and Maxwell’s equations.
Literature
[1] J. D. Jackson, Classical Electrodynamics, Wiley 1980.
[2] A. Zangwill, Modern electrodynamics, Cambridge University Press 2013.
[3] L. D. Landau and E. M. Lifshitz, Vol. 2: The Classical Theory of Fields,
Butterworth-Heinemann 1980.
[4] L. D. Landau and E. M. Lifshitz, Vol. 8: Electrodynamics of Continuous
Media, Butterworth-Heinemann 1984.
11
2 Description of Modules
2.1.4 Electrodynamics 2 (ED2 )
Lecturer
20 lectures
5 tutorials
Class Test
Exam
A/Prof H. Weigert, [email protected]
First semester, second quarter
counting 25% towards module mark
counting 25% towards module mark
2 hours, in May/June, counting 50% towards module mark
Outline
Relativistically covariant formulation of electrodynamics – gauge potentials and
a count of degrees of freedom – electrodynamics as a classical field theory –
Greens functions revisited: Fourier transforms and the use of residues – moving charges and radiation – multipole expansions and spherical harmonics –
electromagnetic waves in vacuum and in media – from electromagnetism to ray
optics and beyond.
Literature
Same as for module ED1 .
2.1.5 Kick-off module (KO)
Activities in the orientation week involving several lecturers and dealing with:
• the nature of physics and physics education,
• mathematical tools and skills for the Honours course, combined with an
introduction to Mathematica, and a Python/VPython refresher,
largely discussion and tutorial-based, with hands-on activities, team work as
well as homework. No grades, but required for the DP certificate.
Outline
Intro to philosophy and nature of physics; Role of mathematics and modelling;
Why is physics hard to learn? (A perspective from cognitive psychology); role
of practical work in learning physics; Learning to think computationally. —
12
2.1 Compulsory and Physics-elective Modules
Introduction to Mathematica; linear algebra and vector calculus; complex analysis; differential equations; Fourier analysis and integral transforms; numerical
methods.
2.1.6 Nuclear Physics (NP)
Lecturer
20 lectures
problem sets
practicals
Exam
Dr T. Leadbeater, [email protected]
Second semester
counting 20% towards module mark
counting 30% towards module mark
in October/November, counting 50% towards module mark
Outline
This module will feature the practical aspects of nuclear physics, in particular detection and measurement of particle and gamma radiation. Topics will
include the basic nuclear processes in radioactive sources, the production of
particle radiation beams, particle accelerators, the passage of radiation through
matter, radiation protection, the general characteristics of detectors, ionization
detectors, scintillation detectors, semiconductor detectors, the statistical treatment of radiation measurements, methods of pulse analysis, spectral analyses,
nuclear electronics, digital pulse processing, applications in nuclear and particle
physics. The module includes five practical exercises associated with radiation
detector design and application.
Literature
[1] G. F. Knoll, Radiation Detection and Measurement, Wiley 2010.
[2] W. R. Leo, Techniques for Nuclear and Particle Physics Experiments,
Springer 1994
13
2 Description of Modules
2.1.7 Physics Education (PE)
Lecturer
20 lectures
2 essays/projects
Exam
A/Prof S. Allie, [email protected]
seminar style format, First and second semester
counting 50% towards module mark
Take-home: 2 essays, in October/November, counting
50% towards module mark
Outline
While most of physics involves learning various content areas such as nuclear,
particle, solid state etc., physics education deals with how we learn physics.
Although physics education has a long history the area called Physics Education Research (PER) is a more recent addition to the sub-disciplines of physics.
For example, since 2005 there is a journal dedicated to PER within the influential Physical Review series, namely Physical Review Special Topics Physics
Education Research (PRSTPER). Several North American universities now advertise posts for lecturers in physics departments who have completed PhDs in
PER. It is also interesting to note that other disciplines such as Chemistry and
more recently Biology are also following this model. This discipline focussed
approach to researching educational issues in science disciplines is referred to
as (Science) Discipline Based Education Research (DBER).
The present course is aimed as an introduction to the area of PE and PER
with a particular focus on issues pertaining to the teaching and learning of
physics at university level. The list below indicates the main themes that will
form the basis of the course. Since the themes are inter-linked the order of
presentation is not linear but should rather be thought of as ‘topic hubs’ in a
network.
• What is Physics?
• Exploring the ‘nature’ of student difficulties
• Issues in cognitive science that could inform understanding the learning
physics
• Teaching physics
• Physics Education Research
Literature will be provided.
14
2.1 Compulsory and Physics-elective Modules
2.1.8 Particle Physics (PP)
Lecturer
20 lectures
5 tutorials
1 journal review
Class test
Exam
Dr S. Yacoob, [email protected]
Second semester
counting 25% towards module mark
counting 10% towards module mark
counting 15% towards module mark
2 hours, in October/November, counting 50% towards module mark
Outline
Classification of elementary particles — Relativistic kinematics, symmetries,
Feynman calculus — Gauge theories: QED, Electroweak theory, QCD — Neutrino oscillations — Beyond the Standard Model.
Literature
[1] D. Griffiths, Introduction to Elementary Particle Physics, Wiley 2005.
2.1.9 Quantum Field Theory (QF)
Lecturer
10 lectures + self study
Dr W. A. Horowitz, [email protected]
Second semester, 4th quarter
(equivalent to 20 lectures)
tutorials
1 independent project
counting 50% towards module mark
counting 50% towards module mark
Outline
Quantizing gauge fields. Fadeev-Popov gauge fixing. Non-abelian fields. Tree
level calculations. Renormalization.
Literature
[1] M. E. Peskin and D. V. Schroeder, An introduction to Quantum Field
Theory, Addison Wesley 1995.
[2] G. Sterman, An Introduction to Quantum Field Theory, Cambridge 1993.
15
2 Description of Modules
[3] L. H. Ryder, Quantum Field Theory, Cambridge 1996.
[4] M. Srednicki, Quantum Field Theory, Cambridge 2007.
2.1.10 Quantum Mechanics 1 (QM1 )
Lecturer
20 lectures
5 tutorials
1 project
Class test
Exam
Dr A. Hamilton, [email protected]
First semester, first quarter
counting 20% towards module mark
counting 15% towards module mark
counting 15% towards module mark
2 hours, in May/June, counting 50% towards module mark
Outline
Examples of quantum systems: semi-bound state [demo] and the Stern-Gerlach
experiment — Mathematical tools of quantum mechanics: Hilbert spaces, Dirac
notation, operators, discrete and continuous bases, matrix versus wave mechanics — Postulates of quantum mechanics: observables and measurements, time
evolution, symmetries and conservation laws, classical to quantum mechanics
— Harmonic Oscillator using matrix mechanics — Angular Momentum: orbital and spin angular momentum, rotations in quantum mechanics, addition
of angular momentum.
Literature
[1] N. Zettili, Quantum Mechanics: Concepts and Applications, Wiley 2009
(primary text, students recommended to have a copy).
[2] J. J. Sakurai, Modern Quantum Mechanics, Addison Wesley 2010.
[3] D. Griffiths, Introduction to Quantum Mechanics, Prentice Hall 1994.
16
2.1 Compulsory and Physics-elective Modules
2.1.11 Quantum Mechanics 2 (QM2 )
Lecturer
20 lectures
5 tutorials
Class test
Exam
Prof A. Peshier, [email protected]
First semester, second quarter
counting 25% towards module mark
counting 25% towards module mark
2 hours, in May/June, counting 50% towards module mark
Outline
Many-particle quantum systems: exchange symmetry, Pauli exclusion principle,
spin-statistics theorem — Approximation methods: time-independent perturbation theory, Fermi’s golden rule, variational methods, WKB approximation
— Scattering theory: Lippman-Schwinger equation, Born approximation, Optical theorem — Path integral formalism.
Literature
[1] J. J. Sakurai, Modern Quantum Mechanics, Addison Wesley 1993.
[2] L. D. Landau and E. M. Lifshitz, Vol. 3: Quantum Mechanics, ButterworthHeinemann 1981.
[3] A. Messiah, Quantum Mechanics, Dover 1999.
[4] R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals,
Dover 2010.
2.1.12 Relativistic Quantum Mechanics (RQ)
Lecturer
20 lectures
5 tutorials
Exam
Dr W. A. Horowitz, [email protected]
Second semester, 3rd quarter
counting 50% towards module mark
2 hours, in October/November, counting 50% towards module
mark
Outline
Relativistic invariance, equations and Lagrange densities for Klein-Gordon and
Dirac and vector fields — Elements of a quantum theory of fields: scalar,
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2 Description of Modules
vector and spinor fields — Particle interactions, simple Feynman diagrams and
scattering matrix; cross sections and decay rates; phase space.
Literature
[1] M. E. Peskin and D. V. Schroeder, An introduction to Quantum Field
Theory, Addison Wesley 1995.
[2] G. Sterman, An Introduction to Quantum Field Theory, Cambridge 1993.
[3] C. Itzykson and J.-B. Zuber, Quantum Field Theory, McGraw Hill 1980.
[4] M. D. Schwartz, Quantum Field Theory and the Standard Model, Cambridge 2014.
[5] L. H. Ryder, Quantum Field Theory, Cambridge 1996.
[6] M. Srednicki, Quantum Field Theory, Cambridge 2007.
[7] L. S. Brown, Quantum Field Theory, Cambridge 1994.
[8] J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics, McGraw
Hill 1963.
2.1.13 Statistical Physics (SP)
Lecturer
20 lectures
5 tutorials
Class test
Exam
Prof A. Peshier, [email protected]
First semester
counting 25% towards module mark
counting 25% towards module mark
2 hours, in May/June, counting 50% towards module mark
Outline
Thermodynamics: extensive and intensive variables, Thermodynamic potentials, Maxwell relations, phase coexistence — Postulates of Statistical Physics:
Phase space of classical and quantum systems, Liouville’s theorem, systems in
contact with each other, ensembles, fluctuations — Interaction-free systems:
harmonic oscillators, Bose and Fermi gases, Bose-Einstein condensation — Interacting systems & phase transitions: cluster expansion and Van-der-Waals
18
2.1 Compulsory and Physics-elective Modules
equation of state, Ising model, mean field approximation, Landau theory, basics of renormalization group approach, numerical simulations.
Literature
[1] M. Kardar, Statistical Physics of Particles, Cambridge 2007.
[2] L. D. Landau and E. M. Lifshitz, Vol. 5: Statistical Physics, ButterworthHeinemann 1980.
[3] R. K. Pathria, Statistical Mechanics, Butterworth-Heinemann 1996.
[4] F. Schwabl, Statistical Mechanics, Springer 2005.
2.1.14 Solid State Physics (SS)
Lecturer
20 Lectures
5 tutorials
2 paper reviews
Class test
Exam
A/Prof M. Blumenthal, [email protected]
Second semester
counting 25% towards module mark
counting 10% towards module mark
counting 15% towards module mark
2 hours, in October/November, counting 50% towards
module mark
Outline
Review of Bulk Semiconductors: Crystal structure, energy band structure, doping — Introduction to Low Dimensional Systems: Length and energy scales,
overview of fabrication techniques and possibilities in nano-physics, applications
of low-dimensional physics — Electron Properties in Low Dimensional Systems:
Band engineering, heterostructures, free electron gas, 2D electron gas, 1D electron gas, 0D electron gas, density of states — Quantum Transport: 1D wires,
0D quantum dots, Coulomb blockade, resonant tunnelling, charge detection,
single-electron dots, electron pumps and turnstiles, surface-acoustic-wave current source — Electrons in magnetic fields: Landau levels, Shubnikov-De Haas
effect, integer quantum Hall effect, edge states, Aharonov-Bohm effect.
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2 Description of Modules
Literature
[1] C. Kittel, Introduction to Solid State Physics, Wiley 1996.
[2] N. W. Aschcroft and N. D. Mermin, Solid State Physics, Holt, Rinehard
and Winston 1976.
[3] M. J. Kelly, Low-dimensional Semiconductors: Materials, Physics, Technology, Devices, Clarendon Press 1996.
[4] J. H. Davies, The Physics of Low-Dimensional Semiconductors: An introduction, Cambridge 1997.
[5] E. L. Wolf, Nanophysics and Nanotechnology, Wiley 2007.
2.2 Additional Modules
Other departments, e. g. Applied Mathematics or Medical Physics, may offer
courses/modules with sufficient overlap to physics, which then could be selected
as additional modules. Consult the course coordinator.
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2.3 Research Projects
2.3 Research Projects
A/Prof M. Blumenthal, [email protected]
Solid state physics, Cryogenics
Measuring pulse tube cooling power.
Cooling samples using cryogens such as helium is becoming prohibitively expensive, especially in South Africa. Pulse tube refrigerators (PTRs) allow dry
cooling (without the need for cryogens) down to a temperature of 4K. The
working mechanism is a variation on a Sterling cooler but without moving
parts. UCT physics has recently installed a dry fridge that is precooled using a
2-stage PTR. The students primary goal will be to design a water or nitrogen
cooling system to be made by the workshop, to measure the cooling power of
the PTR, and assess whether it can be improved by such a system.
Aims: Write a short literature review chronicling the advancements of dry
cryostats. Design and build a cooling system for the PTR. Measure the improvement in cooling power.
Secondary aims: Design and build a working demonstration pulse tube based
on a Sterling cooler.
Prof A. Buffler, [email protected]
Applied nuclear physics
(i) Calibration of a new organic liquid scintillator.
Recently there has been a high level of interest across the world in the use of
well-characterized neutron beams that span a wide range of applications. These
include radiation protection at high-energy accelerators and during space missions, radiation hardness testing of electronic devices, and measurements for
innovative nuclear energy systems. The fast neutron beam facility at iThemba
LABS is recognised as having unique features for application-oriented work, as
well as for neutron physics. Much of the recent work at the iThemba LABS
cyclotron involving fast neutron beams has been within the long and successful collaboration between the Physics Department at the University of Cape
Town and the Physikalisch-Technische Bundesanstalt (PTB), Braunschweig,
Germany. We have recently acquired a new digitally-stabilized organic liquid
scintillator (NE213) which will be used at iThemba LABS for neutron beam
fluence measurements. One of the features of NE213 is that signals associated
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2 Description of Modules
with neutrons and gamma-ray within the detector can be separated using the
technique of pulse shape discrimination. This project will calibrate this new
detector using both gamma-rays and neutrons. Experimental work will be carried out at UCT. An interest in applied nuclear physics and data analysis is a
prerequisite.
(ii) Using PEPT to explore the fluid dynamics of vortex-type flow.
Positron Emission Particle Tracking is based on the tracking of a single tracer
particle which has been labelled with a radionuclide that decays via beta-plus
decay. The location of the particle is obtained by the triangulation of events
associated with the detection of pairs of annihilation gamma rays in a modified
“positron camera”. The trajectory fields derived from PEPT can be employed
to characterise kinematic distributions of the ensembles of flow in very many
contexts. An interesting and very common system of flow is the vortex-shaped
field found in many industrial systems such as cyclones, which are used to separate particles from a gas, for example, and indeed in the typical food blender
found in the kitchen. This project will explore the capability of PEPT to measure the parameters necessary to describe vortex-shaped flow, and use these
measured parameters to comment on the accuracy of analytical descriptions of
such flow fields. The project will require interest in fluid dynamics and include
experiments at the PEPT Cape Town facilities at iThemba LABS. Working
knowledge of MATLAB will help.
em. Prof J. Cleymans, [email protected]
High energy theoretical physics
Transverse Momentum Distributions at the Large Hadron Collider.
Collisions at the LHC produce a large number of secondary particles. These
provide information about the basic dynamics of strongly interacting particles
at very high energies. The project will teach students about measurements at
the LHC and about the interpretation of results. The description of data will
make use of the Tsallis distribution which has been shown to be accurate over
14 orders of magnitude.
em. Prof C. Comrie, [email protected]
Solid State Physics, Microelectronics
Stability of GeSn strained layers during thermal annealing.
At present over 95% of microelectronic devices which are produced are based
22
2.3 Research Projects
on silicon even though many other semiconductors have superior properties. It
has been shown that the mobility of electrons and holes in Si can be improved
by alloying si with Ge, which has a larger atomic size causing strain in the SiGe
layer which alters the shape of the electronic bands thus reducing the effective
mass of the carriers. Germanium has superior carrier mobility to silicon, but the
same effect can be achieved by alloying Ge with tin. Unfortunately the diamond
structure of α-Sn is unstable above 13o C making it difficult to incorporate Sn
in Ge and thermodynamically stable Sn incorporation is thus limited to about
1% – too low to cause the desired properties. Despite these constraints careful
preparation has enabled alloys with Sn levels of around 10% to be achieved.
The thermal stability of these films is however open to question.
Rutherford backscattering spectrometry (RBS) using 2 MeV alpha particle
will be used to monitor the Sn stability in GeSn during thermal annealing while
RBS/channelling will be used to confirm that the layers were indeed strained
by the Sn incorporation, and to establish if any relaxation occurred during
thermal annealing.
Dr T. Dietel, [email protected]
High energy experimental physics
(i) Photon and Neutral Pion Measurements with ALICE.
The ALICE Experiment at CERN’s Large Hadron Collider studies nuclear
matter under extreme conditions: in ultra-relativistic collisions of lead nuclei,
the nucleons are expected to break up or ‘melt’, and a novel state of matter, the
quark-gluon plasma (QGP) is formed. In each collision, only a small amount
of QGP is produced, which expands rapidly before it freezes out into a gas of
hadrons.
Photons provide unique insights into the QGP: thermally produced photons,
similar to black-body radiation, indicate that the temperature in the fireball
reaches several trillion degrees, and prompt photons allow a direct look into the
earliest moments of the collision. A huge background from the decay of neutral
pions complicates the measurements and has to be subtracted on a statistical
basis.
In this project, we will measure photons and neutral pions via their conversion into electron-positron pairs. This method provides the best resolution
for low photon energies and is therefore ideally suited for the measurement of
thermal photons. The resulting photon and pion spectra are the basis for the
statistical subtraction to extract the spectra of direct photons, i.e. photons that
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2 Description of Modules
are not produced in the decay of neutral pions or other hadrons.
(ii) ALICE Transition Radiation Detector.
The Transition Radiation Detector (TRD) of the ALICE Experiment at CERN’s
Large Hadron Collider is a gas detector to measure charged particles and identify electrons. One chamber of the TRD is installed at UCT and gives students
the opportunity to work with state-of-the art detector technology. We plan to
use the chamber in the 3rd year laboratories for the first time in 2016.
The purpose of this honours project is to complete the setup of the TRD
chamber at UCT, use the chamber to record cosmic ray events and analyze
the recorded data. The first part of the projects will require some handson work to commission gas supply and high-voltage power supplies as well as
trigger detectors. In the second part, the existing analysis software will be
enhanced to visualize the recorded events, and we will be able to study the
signals generated by the detector under different conditions and measure some
properties of cosmic radiation, like the angular distribution of cosmic rays.
(iii) Track Reconstruction with the ALICE TRD.
The ALICE Detector at CERN’s Large Hadron Collider will be upgraded in
2019/20 to take advantage of the increasing LHC luminosity and to provide 100
times more events for high precision measurements. As part of this upgrade,
the Transition Radiation Detector (TRD) will receive new readout electronics,
resulting in significant changes in the raw data format to reduce the data volume
to less than 10 gigabytes per second.
In this project, we will reconstruct the trajectories of particles traversing
the ALICE Detector and the TRD, using data as it will be available after the
upgrade. The reconstruction algorithms will have to provide precise estimates
for the particles position and momentum, but also be very fast to process the
incoming data stream of several gigabytes per second. We will use Kalman
filters, which can efficiently handle the different sources of uncertainly, but are
usually restricted to normally distributed errors. A part of this project will be
to find a method to extend Kalman filters to the non-gaussian errors found in
the ALICE TRD.
24
2.3 Research Projects
em. Prof C. Dominguez, [email protected]
High energy theoretical physics
Electromagnetic structure of the nucleon.
The nucleon (proton/neutron) is not a point particle, as it is a bound state
of three quarks. This implies, among other things, that when probed with
virtual photons the nucleon exhibits a non trivial electromagnetic structure. In
technical jargon this is referred to as the electromagnetic form factors of the
nucleon. It provides information on the electric charge and magnetic moment
distribution of the nucleon. At present there is substantial experimental data on
these form factors. The challenge is to predict these form factors from Quantum
Chromodynamics (QCD), the theory describing the strong interactions among
quarks and gluons. The project will deal with comparing theoretical results
obtained in a QCD inspired framework with data. No previous knowledge of
QCD is required. If results are successful (as expected), then this would very
likely result in a publication in a top journal. Previous Honours students who
did similar projects published papers.
Dr A. Hamilton, [email protected], and
Dr S. Yacoob, [email protected]
High energy experimental physics
(i) Searching for Same Sign WW Scattering in ATLAS.
In this project the student will use ATLAS data to identify a class of events in
which two W-bosons are produced with the same electromagnetic charge. These
interactions are extremely rare and have not been conclusively observed before.
This project will require computer programming skills including Linux/Unix
OS, python, and C++. You will work closely with the post-graduate students
working in the UCT-ATLAS group.
(ii) Cosmic Rays.
Investigate the feasibility of a large area ground based cosmic ray detector in
Cape Town. Present day cosmic ray detectors typically carry a very large area
and are composed of hundreds to thousands of individual detectors connected
via GPS. The student will develop a proposal and perhaps prototype of a cosmic
ray detector. This project will require hardware and electronics development
skills (which can be acquired on the job).
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2 Description of Modules
(iii) Cloud Chamber.
The goal is to produce a third year practical using a cloud chamber. While there
are many ways this can be done, the initial idea is to measure the momentum of
particles coming from a radioactive decay using photographic images of cloud
chamber tracks in a magnetic field. Previous students have created a working
cloud chamber, the complete project will require development of magnetic field
and data acquisition system. This project will require hardware development
and creativity.
Dr W.A. Horowitz, [email protected]
High energy theoretical physics
(i) Phenomenological AdS/CFT.
Apply the methods of the anti-de-Sitter/conformal field theory correspondence
to compute observables in high energy nuclear collisions at RHIC and LHC. Use
string theoretic techniques in 5 dimensions to gain insight into the physics of
strongly-coupled field theories in 4 dimensions. There are many excited ways
in which this project may go. One may numerically compute predictions of
observables at RHIC and LHC with stochastic differential equation solving in
a Langevin approach; one may also numerically propagate initial conditions
through a coupled set of PDEs to the boundary of the 5D anti-de-Sitter space
to compute the energy momentum tensor related to high momentum probes
of strongly-coupled plasmas. Or one could derive analytically the energy and
momentum lost by high velocity probe particles corresponding to strings with
finite endpoint momenta.
(ii) Ultrarelativistic Nuclear Tomography.
Demonstrate the efficacy of the next generation particle collider in directly
measuring the distribution of matter in ultrarelativistic nuclei using exclusive
vector meson production. Determine whether experiment can distinguish between various theoretical models for the nontrivial, emergent phenomena in
very dense, very energetic nuclei. Improve calculations with a derivation of the
next-to-leading order corrections to the scattering formulae.
(iii) Energy Loss in Perturbative Quantum Field Theories.
Derive formulae for the energy lost by high momentum particles propagating through weakly-coupled plasmas in thermal field theory. Extend past calculations to include next-to-leading order corrections due to the emission of
26
2.3 Research Projects
very high energy particles, particles at large angles, and in coupling. Find
the changes to the energy loss formulae due to a flowing medium. Adapt the
techniques of maximal helicity violating diagrams to multi-gluon emission in
radiative energy loss process in high-energy nuclear collisions.
Prof A. Peshier, [email protected]
High energy theoretical physics
(i) Equilibrating the quark-gluon plasma.
A key question arising from experiments at at CERN’s Large Hadron Collider
is: How can the quark-gluon plasma (QGP), which is produced in heavy-ion
collisions in an off-equilibrium initial state, approach local equilibrium in a
short time of the order of 10−23 s. We will seek to gain insight into this challenging topic at the interface of Quantum field theory and Statistical physics
by exploring the QCD Boltzmann equation, a non-linear integro-differential
equation. In particular, we will calculate the shear viscosity of the QGP, which
describes how fast laminar flow patterns relax to equilibrium, in order to understand why the QGP is called the most perfect fluid.
(ii) Beat the traffic.
This is an interdisciplinary project, co-supervised with Prof A. Buffler, Physics,
Prof K. Naidoo, Scientific Computing Research Unit, and Prof I. Barashenkov,
Applied Mathematics (we are all not amused about the daily traffic jams). We
will identify a relevant region in Cape Town to first analyze and then model
various traffic phenomena by methods of statistical physics. The ultimate goal
is to come up with specific proposals, to be made to the City of Cape Town, to
ease (hopefully by simple and affordable means) the congested traffic situation.
Dr S. Peterson, [email protected], and
A/Prof M. Blumenthal, [email protected]
Nuclear physics and cryogenics
Build Nuclear Orientation Thermometry system for new ultra-cold dilution refrigerator at UCT.
Background: Nuclear Orientation (NO) Thermometry is a technique that
uses the polarization of Co-60 atoms at ultra-cold temperatures (< 50mK)
to determine the temperature of the system. As the temperature inside the
fridge (and the source) drops below 100mK, the spin of the Co-60 atoms lose
27
2 Description of Modules
their mis-alignment (due to thermal fluctuations) and emits the two characteristic gamma-rays (1.17 and 1.33MeV) along the axis of the crystal (instead of
isotropically). By comparing the spectra along the crystal axis and perpendicular to the crystal axis, it is possible to accurately determine the temperature
down to 5mK.
Objective: This goal of the project is to build a NO Thermometry system
using a standard Co-60 calibration source and two NaI scintillation detectors
that can be used to determine the temperature of the fridge.
Dr D. Taylor, [email protected]
Physics education
Physics Education Research investigates the teaching and learning of physics.
Students make sense of what happens in a physics course based on their individual make-up and past histories, and as a result their learning outcomes are
often different from those intended by their lecturers. Thus within a class there
may be considerable variation in how students understand a particular concept.
Phenomenography is a research approach sometimes used in Physics Education
Research which explores the variation in the conceptions which a group of people have of a particular phenomenon. Examples of phenomenographic studies
can be found online, for example:
[1] Ebenezer, J. V., & Fraser, D. M. (2001). First year chemical engineering
students’ conceptions of energy in solution processes: Phenomenographic
categories for common knowledge construction. Science Education, 85(5),
509-535. doi: 10.1002/sce. 1021
[2] Ingerman, A. (2003). Expounding on physics: a phenomenographic study
of physicists talking of their physics. International Journal of Science
Education, 25(12), 1489-1508.
[3] Marshall, D., & Linder, C. (2005). Students expectations of teaching in
undergraduate physics. Int. J. Science Educ., 27(10), 1255-1268.
(i) Demonstrators conceptions of a lab report.
The laboratory report is the primary piece of writing expected by physics undergraduate students. In the physics department, these are marked by demonstrators who are post-graduate students with a variety of different backgrounds.
28
2.3 Research Projects
The research question for this project is: What conceptions do physics demonstrators have of a laboratory report? The data for this investigation will be
lab reports which demonstrators will have produced, on the same first year
experiment. The results of this research project will inform future training of
laboratory demonstrators.
(ii) Variation in student understanding of a physics concept.
For this study, the student will choose a suitable physics concept / phenomenon,
for example fields (electric, gravitational etc) or time dilation – the actual concept to be studied will be chosen in consultation with the honours student, and
should align with the students own interests. The student will perform a phenomenographic analysis of an undergraduate UCT physics classs conceptions
of this phenomenon. The class should have studied the concept already. The
research instrument will be open-ended written responses or interviews.
A/Prof H. Weigert, [email protected]
High energy theoretical physics
(i) Why pions are (almost) massless (and protons are heavy).
The mass of observable (non-dark) matter is almost entirely due to a phenomenon called (spontaneous) chiral symmetry breaking. This is the phenomenon that predicts (almost massless) pions and heavy baryons such as protons. Descriptions of this range from the MIT bag model through effective field
theories to QCD. The project is meant to explore part of this, depending on
interest of the student.
(ii) Instantons in QCD: From topology to nontrivial ground states in field QCD.
This aims at a qualitative understanding of the vacuum ground state of QCD,
the theory of strong interactions. The vacuum of field theories is generically
not an “empty thing devoid of content”. A familiar example might be the all
permeating Higgs field that gives masses to W and Z bosons (and tiny current masses to fermions). The vacuum of QCD is even more complicated and
built around nontrivial gauge configurations with definite topological winding
numbers that are essential in qualitatively qualitative features of QCD bound
states. The project’s goal is to explore this set of ideas and present it at an
elementary level.
(iii) Berry phases: topology of space induces new phenomena and makes gauge
potentials observable.
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2 Description of Modules
In “conventional” settings, only E and B fields are observable quantities, the
gauge potential (which can be changed at will by adding total 4-divergences)
remains unobservable. This changes drastically if defects in space (lines excluded from accessible space) are introduced. The defects impose constraints
on the allowable gauge transformations of the gauge potential and make gauge
phases observable in certain experiments.
30
3 Lecture time table
The time tables below are drafts and might be changed to avoid
clashes with modules from other departments.
For updates as
well as a detailed course calendar, please check the course web site
www.phy.uct.ac.za/courses/phy4000w.
All Physics courses will be given in the RW James Building.
First semester
The CM and SP tutorial sessions are biweekly, on alternating Wednesdays.
Second semester
The SS/NP and CP/NP tutorial sessions are biweekly, on alternating Wednesdays and Fridays, respectively. The RQ module runs in the first half of the
semester (3rd quarter) with 4 lectures per week and one tutorial, the QF module follows in the second half of the semester (4th quarter).
31