At the moment, I am trying to help out Prof Lee to do a simple numerical calculation for his high Tc model, called it extended Hubbard Model (EHB) [1]. In my opinion, and in many's as well, Prof Lee is among the best physicists in Malaysia. he has very sharp insight in the physics in condensed matter physics, and he prefers more theoretical construct rather than on the computational aspect.
For a 'newbie' physics researcher is looking for a good theoretical topic to work on, Prof Lee's high Tc model is a very attractive research topic. He is a very senior researcher who knows very well the details of the high Tc modelling tools, and he has a very sharp insight on how to proceed with the modelling of the high Tc physics. I am trying to learn from his seniority experience, and also hoping to 'leap off' from his experiences in condensed matter physics, which is not a field of my expertise. The research issue here is to model the behavior of high Tc superconductivity and pseudo gap in cuprate oxides. Many models exist. Prof Lee's pick is the more conventional one based on BCS-like mechanism of phonon-electron interactions, albeit not entirely similar in nature. In his proposal, a non-harmonic terms in the phonon-electron enter the hamiltonian, providing an explanation to the pseudo-gap and Fermi arc seen in high Tc cuprates. From personal point of view, I take my involvement in his the research an opportunity to leap into a real impact research topic by standing on the shoulder of a giant. This is a high impact topic, initiated by our very own local expert to take on a frontier research challenge.
Hubbard model is the theory that describes Mott insulator very well. In [1], a new term due to non-linear mode between the phonon and electron was added to induce a d-wave symmetry, which is observed in experiments. There are other very attractive features about Prof Lee's model as well. i didn't realise the beauty of it until i myself make a literature search about the high Tc model in cuprate oxide (Nature physics, Vol 2, March 2006).
Apart from the physics argument justifying the physical origins of the terms in his model, technically, the calculation proceeds along the following way: Build the hamiltonian -> Propose a trial hamiltonian --> Construct the trial free energy --> Use Bogolyubov variantional pricinciple to minimise the trial free energy --> The minimisation results in equations relating various quantities of physical interests, and from here one can determine, say for example, the critical temperature as a function of dopant concentration. The whole machinery is based on the Bogolyubov variational principle, a very powerful theoretical tool used by people in condensed matter physics. The trick here is to be able to guess the appropriate trial hamiltonian, which requires one to have very strong physics insight about the system under investigation. Prof Lai praised highly of Prof Lee for being able to have such a sharp insight to write down the trial hamiltonian for a non-trivial system. The more insight you have on the system, the trial hamilonian constructed would give a more realistic description of the physics of the system.
How about the exact values of the coupling constants in the Hubbard model? In fact the effective coupling constants in the case of his extended Hubbard model are arbitrary parameters. These are the 't_ij' and 'U' terms. The former represent 'tunnelling' or hopping of an electron from site i to nearest neighbour j (this corresponds to attractive interaction between neighbouring atomic sites), whereas the latter term represent the 'on-site' repulsive interaction when electrons stay on the same ionic site. These are the essential features of the Hubbard model. In the EHB (extended hubbard model) of Prof Lee, these interaction are not known. In my computational calculation I will provide a set of values representing these t_ij and U, then solve the gap equation as a function of temperature and dopant concentration. The gap equation is obtained as a result of the minimisation of the trial free energy using Bogolyubov variation method. What we wish to obtain is the 'superconductivity dome', the critical temperature curve vs dopant concentration, which has been measured experimentally. So if we could some how reproduce such a 'dome' and show it to match with experimental data, we are on the right course towards a full description of high Tc superconductivity in cuprates.
The modelling of full features of high Tc in cuprates involve many stages, each requires independent pieces of new ingredient. The other features needed are e.g., the pseudogap curve, and magnetic order of high Tc, isotope effect, plus others stuff that i am currently ignorant of. Some of these features could be independent, some could be due to a common physical origin. No one knows for sure at the moment. We can't provide a complete accounts to all the experimental features of high Tc in cuprates in a single shot due to the immense difficulty in the modelling. So we have to go by stages.
Take the high Tc cuprate as a big zig saw puzzle. we are now assemble the pieces one in a step, with the hope to complete the whole puzzle at the end. The modelling process reminds me of of the construction of any extension of the Standard Model to incorporate neutrino anomalies when writing my PhD thesis.
Reference:
[1] B. S. Lee, J Supercond Nov Magn (2010) 23: 333-338. Non-linear localised lattice mode coupling mechanism and the pseudogap in high-temperature superconducting cuprates.
11.11.10
Think like a physicist
Physics has been a difficult subject not only to students but also to the teachers. There have been many causes leading to such impression, such as the structural deficiency in our education systems and the poor appreciation for an intellectual culture. The university education in many ways is simply yet another secondary school sitting in a larger campus. Students memorise the formulas and concepts, vomiting them out again in the exam halls, but never appreciate the intellectual process of how these concepts are formulated. To many students physics is merely a collection of formulas that can be used to calculate certain problems. When given a physics problem, what first come to their minds is to scan for the right formula from their memorised data base, instead of analysing it with a more robust approach. Such a mechanical practice is a norm among the students and has saved many’s “lives” in the exam halls. But it has also deprived them the opportunity to think like a physicist.
In a typical classical mechanics course for example, various “must know” concepts or theories are taught, such as how to describe the translational and rotational motion of a point particle or a rigid body, the classical concepts of forces, gravity etc. These are specific knowledge that has to be learned by students (and to be tested in the exam hall). However, these specific concepts and theories are different in nature from the more general, and somewhat more abstract, aspect of the physics methodology used to formulate them. At this point, I would like to make a distinction between physics concepts (or theories) and physics methodology, a.k.a. “the way how physicists think”, or “physicist’s paradigm”. Teaching physics and mathematics should not only involve presentation of fact, concepts, formulas and technique to perform calculation. Equally important is to teach the students how to think like a physicist.
Physicists’ paradigm is characterised by clear logic. They think along a logical track when formulating a quantitative description of a physical system. They are able to distinct one line of logical thread from the other, and see the connection between them. Logics are spoken in the language of mathematics, hence physicists are intensive users of mathematics. They have to translate an idea or a theory precisely using the language of mathematics because physical reality is represented using mathematical symbol and equations in physics. Physicists must know how to abstract information from observations and put them coherently into a mathematical form for further logical manipulation. They do experiments on a physical system and make measurement, then use mathematics to build model to describe the physics as inferred from the experimental data. Physicists have to make smart simplification when building models to describe a physical system. They need to know how to deduce physical consequences or inferences from a set of mathematical equations. They often apply tricky mathematical procedures such as making approximation at different levels of accuracies when approaching a complex system. Very often they need to be smart enough to spot the underlying similarities between two disparately different systems so that the theoretical treatment used for one system lends a helping hand to describe the others. Sometimes physicists simply have to be clever enough to put forward a smart guess to tackle a clueless problem. The set of methodology used by physicists as briefly mentioned above is an art practiced by all, yet is not mentioned explicitly in most physics textbooks. It is only to be acquired after a long time working in the physics research business. Making student to at least be aware of the physicist’ paradigm is one of my agenda in my teaching.
When I teach physics, of course I will explain the mathematical formulas and theories, or illustrate the physical laws by working examples, as every physics teacher will conventionally do. On top of that, I also insist on explaining the way a physicist thinks, and the physicists’ methodology when dealing with a physics problem. This, I reckon is an aspect less emphasised by most physics teachers who used to feed the students with formula without properly explaining their origin or the thinking process behind them. Our education system inclines to force students to memorise the outcome of the thinking process (i.e., the formulas formulated by the physicists) but never teach them to appreciate and comprehend the thinking process itself. Having said that, to teach and train students to comprehend the physicist’s thinking are no easy task. Translating a physics concept into a mathematical form is an abstract and highly intellectual process. To apprehend the paradigm requires certain level of intellectual maturity. I myself was not even aware of the existence of such paradigm when I was a physics undergraduate. The usual way to teach the paradigm is by ways of examples, in which I elaborate and commentate on the process and approaches used by physicists when solving a specific problem. I reckon that the inclusion of physicist’s paradigm in my teaching makes me slightly distinct from other physics teachers.
Moodle: The online learning management system
In the earlier years I built my course websites in the server in the School of Physics
One of the very useful services offered by Moodle is the online assignment submission function. Lecturers can enforce the deadline for last submission, grade the assignments online, and display the grades very conveniently. This means of assignment submission is efficient, saves papers (and trees). I reckon that every lecturer who requires their students to submit assignments should all do it via the Moodle as a contribution to saving the Earth.
The Moodle also provides a function called ‘Wiki’, in which students can freely edit an encyclopaedia-like entry related to a particular concepts or keyword related to the course. Students are encouraged to edit or add in Wiki entries, so that the content of these entries can be perfected over time as a result of collective effort. This is such a wonderfully new concept for teaching and learning, thanks to the brilliant invention of the Wikipedia model. I tried to encourage the use of Wiki in my calculus and linear algebra course once. Except a few rare enthusiasts, the Wiki drew little response from the students, probably due to the lack of familiarity to edit Wiki entries (so was I a stranger to edit Wiki entries). Anyway, I gave it a go but failed to achieve any admirable effect. Despite the failure experience, I reckon editing Wiki by students as a strategy for collective learning could be very effective if it is properly made used of.
Complimenting a course with a website is not the most important factor for a successful teaching. Nevertheless the adoption of such a smart means, as I have experienced it first hand, certainly helps to make good teaching a more plausible task.
Course websites
The first website I build was for the course ZCT 104 Modern Physics back in 2003. It was also the first course I taught in USM. Back then having websites for the courses were not a norm in USM main campus albeit the fact that many overseas universities already practiced course websites as early as mid 90s. I took the difficult first step to build my first course website in spite of the unfavourable conditions then. As late as 2007, USM finally pushed for the implementation of Moodle, an online web service where lecturers can drag-and-drop course-related material online fairly easily. I reckon they should have done that much earlier.
I insist on having a website for each course I teach because that is the way to go for effective and efficient course material management. By now I have accumulated many course websites, which are archived in my person webpage. These are documented teaching experience and activities I had practiced throughout many years in my teaching career, accessible by anyone anytime and from anywhere just a click away at http://www2.fizik.usm.my/tlyoon/teaching. The archive serves the purpose as a reference for my present students who wish to peek into the teaching activities in previous semesters. It offers the historical information of how the same courses were conducted in the past, thus preparing the present students psychologically what to expect in the present semester. In particular the students find it interesting to read about the discussions held by their seniors in the forum of the same courses in previous years. As these discussions were specifically revolved around a particular course they are currently studying, there is a sense of relevance when the present students read them. This contributes positively to the process of teaching in the class. Reflecting my core belief in transparency and liberalism, all of the course webpages I put up are configured to be viewed freely by anyone in the world without the need to key in a password.
Ideally, I try to make it such that students can access all possible information related to the course online for everyone’s convenience. Such practice saves me the trouble to reply students’ SMS request, e.g. where and when will a test happen, or what topics are to be tested. With the course websites fully loaded with essential information, students have no reason to complain of having insufficient material for their learning purpose.
Transparency is the core guiding principle when I put up the course websites. All information is supplied transparently. The essential contents include:
- Synopsis and course-related information. This includes the course synopsis, all relevant information such as the reference text books, exam format, important dates (tests, holidays, extra classes), lecture-by-lecture schedule, criteria for grading, advices and best practices for the course, etc.
- Electronic copies of lecture notes and the latest tutorial problem sets.
- Past year questions, usually completed with full solutions and marking schemes. The inspiration when designing the exam questions are usually derived from various reference sources (mostly the text books and test banks). In the solution schemes, the sources of the exam questions often will be quoted. My purpose is to provide transparency to the process of how I designed the exam questions. This offers the students a window to track their lecturer’s thinking path when designing the questions. I reckon that such information is beneficial to the learning process for the students.
- Latest solutions to the quizzes. These are uploaded, usually immediately right after the quizzes. The immediate release of the electronic solutions is a spree to the eager students who can’t wait to know the solution to the quizzes they just sat.
- All-in-one course material. I take the trouble to electronically bind all the latest lecture notes, tutorial questions, past year solutions and other course-related material into an all-in-one pdf version, which are then uploaded to the course website. In addition, I would also send the softcopy to the photocopy shop so that the students can purchase the hardcopy there.
- Announcement. The course websites are the best place to make announcement. News spread in the cyberspace almost faster than the speed of light these days. Dear (many) teaching academics in USM, still sticking paper notices outside you offices in this Web.2 era?
- Records of past year performances of the courses. These include the records of the grade distribution and the formal reports of the overall exam performance. The formal reports contain information like weakness of the students and the comment made by the lecturer on the overall course performance. These are all “confidential” information not usually available but are very much sought after by students. When made publicly known, the historic statistics with an average 45% failure rate in the last two academic sessions sends the strong message: If you don’t want to be part of the statistics, you better start working now. It is a psychological trick I use to ‘motivate’ the students, albeit in a threatening manner.
- Forum. This is one of the most important components in the course websites. It is the main attraction for students to visit the course webpages. Here, students read their peers’ posting, chit-chat, ask stupid questions, or simply drop a line for fun. Some ask serious questions, debate over certain opinions, or seek quick answers to their assignments. I am usually the central participant in the forum, aided by the occasional appearance of a few active online students to heat up the ambience. A typically reserved student could turn out to be quite out spoken and daring when going online. Meeting and discussing physics with the students in the cyberspace paves an alternative channel to interact with them. The students get to know my character and personal style better if they bother to read my postings on the online forums. It is of my opinion that a student’s awareness of his / her lecturer’s personal trait and teaching style helps to boost the learning and teaching experience. To encourage participation I maintain a free speech policy in the forum. As long as their postings do not violate the obvious social constraints, I never interfere. All kinds of topic are sanctioned, such as advertisement, expression of fear for the courses, or even blatant objection to my teaching style. I try to talk like one of them, using the SMS-like or even broken language to make them feel comfortable to express online. Maintaining an active course-related forum has many obvious advantages to jack up the students’ interest about the course. However, involvement in a heated forum could take up around one to two hours per day of my precious time.
What it takes to be a good physics teacher
I was recruited as a lecturer to the School of Physics
In my opinion, a physics teacher who can make physics comprehensible requires a few qualities: he / she must master the effective techniques in delivering ideas, the knowledge of the subject matter, and to have a passion to deliver the first two. You can’t be a good physics teacher if you lack any of these. For example, P. A. M. Dirac, one of the most important physicists in history and whose contribution to physics is at par with that of Einstein, is said to be the most boring physics teacher. He used the most economical and concise mathematical language to lecture physics to students, but never bother to elaborate further in plain language. Most were left in a state of confusion when Dirac left the class. As physicist, Dirac has the most profound insight for mathematical beauty in a physics theory, but he has not the passion to deliver what he apprehended to grass-root level physics students. On the other hand, one can never teach beyond the level of his understanding. If that is how much one knows, that’s about how much one can teach. In the teacher-centered setting, this would mean a good physics teacher is logically impossible if he / she know too little of the subject matter.
In practice, many physics teachers merely spoon feed formulas which are to be blindly memorised by students, and recycle past year questions in the final exams. The level of comprehension of the core ideas are not usually tested rigorously. In many instances, exams mostly require students to vomit the model answers as memorised. The ability to score the highest grades in physics exams is rarely translated into a reasonable comprehension of the complete idea behind what they have memorised. In my personal opinion, the best way to show whether learning has truly taken place is to demonstrate the ability to apply the knowledge content in research projects, and to correctly explain them in such a manner that others can comprehend them. It is also in this spirit Feynman defined a person to have truly understood a physics concept.
Teaching physics to a class of undergraduate students finally boils down to how to convey a foreign, and often abstract, concept to the audiences. To achieve this, various effective techniques and tricks can be innovated. Throughout the last few years as a physics teacher, I have innovated various tricks and techniques to make undergraduate physics a comprehensible subject. Along the way, I feel deeply that to deliver good teaching I must know my subject matter well. Not only that. Genuine motivation from within is also a mandatory fuel to make me stayed innovative. Innovative methods in teaching may be merely strategies or convenient tools dressed up by fancy technologies. But what essentially drives the implementation of these tricks is personal passion. [1] For the wonderful life of Richard Feynman, see the bibliography by James Gleick (1992). Genius. Vintage Books. Feynman’s three-volume Feynman Lectures on Physics (1964) published by Addison-Wesley is a legacy that has strongly influenced three generation of physicists since the 1960s.
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