Theoretical Condensed Matter Physics
Ph.D., Harvard, 1983.
I work on several topics, the common thread being geometry. Most of my problems involve nontrivial patterns in space; frequently the problem is to determine the qualitative nature of the ground state (or equilibrium phase).
Assisting staff in Physics 214 (access course website via Blackboard)
In past years, I've assisted in introductory courses Physics 101-102, 207-208, 214, and (once) P213. Also, I used to teach undergraduate Solid State (P454).
Taught in spring 1991-93, 1997-99, 2003, 2005, and 2007).
Taught in fall 1989, 1992-93, 1995, 1998; version w/some biological topics 2001, 2003, and 2007. See the poster for topics.
Modular course taught by LASSP theory faculty. Modules I taught
Undergrad projects: I have ideas for projects in theoretical solid-state physics, not using quantum mechanics and related to my quasicrystals, biological physics, or frusrated antiferromagnets research (see "Research supported by the DOE", below). For more details, click here Grad research opportunities: see here . Postdocs: Sorry, I don't usually have funding for a fulltime, two-year postdoc.
Typically on the computational-analytic borderline, with a focus on: what are unbiased ways to get information out of the (experimental or numerical) data? There are two threads currently:
Past projects under (1):
(1) Statistical physics (classical and quantum) of frustrated antiferromagnets on the Kagome and related lattices. These complex antiferromagnets have nearly degenerate ground states, and it is challenging to figure out how small perturbations single out one of them as being the true ground state, or produce an exotic disordered state which is a superposition of many configurations. (Recent theses, Uzi Hizi '06; current undergrad, Sophia Sklan '10).
In the systems I study, the spins have length > 1/2. Thus the naive approach (as works in most magnetic systems) is to expand around the classical ground state -- but which ground state? since they are highly degenerate. Hence it's necessary to set up a perturbation theory to expand around an unspecified state. A common phenomenon in the business is "order by disorder": that means the degeneracy gets resolved (and long-range order develops) precisely due to the strong fluctuations associated with the degeneracy, or perhaps due to quenched randomness (e.g. substitution of the moments by nonmagnetic ions). Uzi Hizi (PhD '06) worked out how quantum fluctuations resolve the degeneracy of the spin-ordering pattern of pyrochlore antiferromagnets.
(2) Height models -- I've also studied 2D discrete models with "height" (interface) representations, which connects to the theory of exact solutions and to conformal field theory (past collaborators Dr. Jane Kondev and Dr. Chen Zeng.) Such models are currently used in toy models of highly frustrated and/or exotic kinds of order, in (a) quantum systems [See "From classical to quantum dynamics at Rokhsar-Kivelson points" , or (b) three-dimensional systemsQuasicrysstals are complex metal alloys with highly ordered, yet non-periodic structures. We want to determine their structure and understand why they form. Thus our work breaks down into (1) atomic structure fitting and structural energies; (2) random tiling ensembles;
(Senior collaborator: Dr. Marek Mihalkovic, Slovak Acad. Sciences. Prof. Richard Hennig (Cornell Materials Science Dept.) did a project with me as part of his Ph.D. thesis (2000) from Washington U. Past undergrads: Nan Gu '05, Sejoon Lim '08; current undergrad, Amulya Bhagat '10) My colleague, Prof. Veit Elser, was formerly active in quasicrystals about quasicrystals.
On the atomic scale, we try to use microscopcially-derived effective potentials to resolve details of the atomic arrangements which would be unclear from diffraction fitting. With Dr. Marek Mihalkovic (from Slovakia and Chemnitz, Germany) and Prof. Mike Widom (Carnegie-Mellon University), we have built a successful computer model of decagonal AlNiCo in this fashion: see the preprint "Total-energy-based prediction of a quasicrystal structure" , by Mihalkovic et al., or a related preprint by C.L. Henley, M. Mihalkovi\v{c}, and M. Widom, In 2004, this work was extended to the Co-rich phase of d(AlCoNi) by Nan Gu (undergrad '04) (see an example image of the idealized atomic pattern found by this simulation.)
I work on two major topics in biological physics They involve statistical mechanics plus spatial patterning.
By what physical mechanism did life break chiral symmetry? Obviously, an ancient symmetry-breaking led to the handedness of biological molecules, but it's nontrivial how this gets expressed at the level of a multicellular organism. Examples are (1) bilateral asymmetry in vertebrate animals (why isn't your heart on the right side?), and (2) spiral growth in plants.
In the past I worked on statistical physics topics of self-organized criticality and on percolation (that includes a bit on cluster-update algorithms).
I belong to the Cornell Center for Materials Research. I was once active in a research group within the CCMR on "Energetic Surface Processing", which involved models of the growth of crystals by atom deposition. (see above)