Mathematical Physics Seminar


January Schedule




Organizer: Joel L. Lebowitz
lebowitz@math.rutgers.edu


Speaker: Elliott H. Lieb, Princeton University

Date/Time/Place: Thursday, January 24, 2008 12:00pm Hill 705

Title: Remarks on Density-Matrix-Functional Theory

Abstract: Density functional theory is moving towards a more complicated version called Density-Matrix-Functional Theory, of which Hartree-Fock theory is an old example. A modification of Hartree-Fock theory due to Mueller is now being used by several researchers. The mathematical foundations (existence and uniqueness of energy minimizers, etc.) are, however, more complicated than for Hartree-Fock theory; in work with R. Frank, R. Seiringer and H. Siedentop we have been able to address the most important questions, but some interesting ones still remain. Phys. Rev. A {\bf 76}, 052517 (2007). arXiv:0705.1587.




Speaker: Thomas Spencer, Institute for Advance Study, Princeton, NJ

Date/Time/Place: Thursday, January 31, 2008 12:00pm Hill 705

Title: Random band matrices and statistical mechanics

Abstract: We present a statistical mechanics model with a hyperbolic supersymmetry. This model is expected to qualitatively describe properties of random band matrices in N dimensions eg localization and delocalization. The "spins" in this model may be thought of taking values in a Poincare super-disc. In three dimensions we show that this model has a diffusive phase. In one dimension there is only the localized phase. The analysis of this model relies a family of identities coming from SUSY together with estimates of a random walk on a percolation cluster. The surprising relation of this model to linearly reinforced random walk will also be highlighted. No knowledge of SUSY is needed. This is joint work with M. Disertori and M. Zirnbauer.