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.