Condensed concepts
Ruminations on emergent phenomena in condensed phases of matter
Quantum frustration in a nutshell
Understanding lattice models for strongly correlated electron systems is a major challenge. Widely studied (and still poorly understood) models include the Hubbard and Heisenberg models. But some insight can be gained from studying model Hamiltonians on small clusters such as four lattice sites. Although, such a small system is far from the thermodynamic limit, these models can illustrate some of the essential physics associated with the interplay of strong electronic correlations, frustration, and quantum fluctuations. They illustrate the
quantum numbers of important low-lying quantum states, the dominant short-range correlations, and how frustration changes the competition between these states.
Furthermore, understanding these small clusters is a
pre-requisite for cluster extensions of dynamical mean-field theory and rotationally invariant slave boson mean-field theory which describes band selective and momentum space selective Mott transitions. See for example my
earlier post on that.
I now give a concrete example which illustrates how frustration can change the quantum numbers of the ground and first excited states. This is taken from a 1996
PRL,
Plaquette Resonating valence bond ground state of CaV4O9, by
Ueda,
Kontani,
Sigrist, and Lee. They first consider a single
Tough times for science in California My wife brought to my attention an article in the New York Times about the consequences of California's budget woes for the University of California system, and especially Berkeley. People interviewed include Bob Birgeneau (famous for inelastic neutron scattering studies of strongly correlated electron materials, now Chancellor at Berkeley) and Richard Mathies (pioneer in femtosecond spectroscopy, now Dean of the College of Chemistry, Berkeley)
Teaching high school physics Dr Richard Walding gave some insights into the current state of high school Physics teaching in Queensland at the AIP Careers seminar on wednesday. He was Head of Science for the past 20 years at Moreton Bay College and now tutors Senior Physics student teachers at Griffith Uni. Richard said tha the demand for physics teachers was very strong, not only here in Queensland but everywhere in the word. Teacher recruiting companies have an unmet demand for physics teachers and it would seem they can place you at countries all over the world. Richard said the starting wage for a graduate was about $51,000 rising to $72,000 after 7 years or so. He said there were 7000 Senior Physics students in Queensland in Yr 11 and 12 from 176 schools and taught by about 220 physics teachers. Most of the teachers had BSc degrees but, surprisingly enough, only a handful majored in physics at university.
To a question about whether you'd have to teach other subjects beside Physics and Junior Science if you were employed as a Physics teacher, Richard said that from his knowledge you may get some Junior Maths but would be unlikely to get anything else unless you asked for it and had been trained for it in your PostGrad Education qualification (e.g. Senior Maths). Richard made the point that teaching didn't suit everyone and some student teachers drop out either during their coursework or soon after. He said he had several former scientists and engineers as student teachers who wanted to become Physics teachers and in most cases they were a success; however, some retuned to their former profession within a year or so as it wasn't what they expected.
Richard said that he never planned to be a Physics teacher; he started his career as an Industrial Chemist but became a teacher after 5 years in industry. As he had physics in his degree the Principal of his school made him take Senior Physics even though he did not do it in his GradDipEd degree. He said he grew to enjoy it and has taught it for the past 30 years. He also said that there was plenty of scope for original research while teaching. He undertook an MSc, MPhil and PhD to satisfy his curiosity about aspects of science education and he said that many teachers were doing postgrad studies (Masters and Doctorates) as part of their Professional development and to help with their promotion prospects. Richard said that a Senior Teacher's wage is $75000 and a Head of Department from $84000 to $88000 - although the recent pay deal would see that increase by a further 8% or so over the next 3 years.
He stressed that Physics teaching may be different today that it was when people in the audience were in high school. There was more emphasis on extended experimental investigations and the report writing that entailed, and with more questions and situations involving evaluating and justifying conclusions (than with the older style emphasis on quantitative, algorithmic, closed problem solving questions). He said it would be worth having a look at the 2007 Senior Physics syllabus to get a better idea. This is available online at http://www.qsa.qld.edu.au/learning/1964.html
Richard is also co-author of a
high school physics textbook,
that Joel Gilmore (Science communicator extraordinaire and my former Ph.D student) was so impressed with he bought it off a student he was tutoring when she finished high school!
Our tendency to scientific fantasy not reality More great quotes from Bob Laughlin, A Different Universe: Reinventing Physics from the Bottom Down
“The great power of science is its ability, through brutal objectivity, to reveal to us truth we did not anticipate.”
(p. xvi)
``mythologies are immensely powerful things, and sometimes we humans go to enormous lengths to see the world as we think it should be, even when the evidence says we are mistaken.’’
(p. 114)
“ideologies preclude discovery. All of us see the world as we wish it were rather than as it actually is.”
(p. 116).
There are similarities to the cautions of Walter Kauzmann, in his Reminiscences of a Life in Protein Chemistry.