Physics – Condensed Matter
Scientific paper
1996-11-28
Proceedings of Advanced Quantum Field Theory Conference in September 1996, Lalonde les Maures (France)
Physics
Condensed Matter
23 pages, LateX, ps file available at http://cpth.polytechnique.fr/cpth/rivass/articles.html
Scientific paper
10.1016/S0920-5632(97)00420-9
In this paper we describe a strategy to study the Anderson model of an electron in a random potential at weak coupling by a renormalization group analysis. There is an interesting technical analogy between this problem and the theory of random matrices. In d=2 the random matrices which appear are approximately of the free type well known to physicists and mathematicians, and their asymptotic eigenvalue distribution is therefore simply Wigner's law. However in d=3 the natural random matrices that appear have non-trivial constraints of a geometrical origin. It would be interesting to develop a general theory of these constrained random matrices, which presumably play an interesting role for many non-integrable problems related to diffusion. We present a first step in this direction, namely a rigorous bound on the tail of the eigenvalue distribution of such objects based on large deviation and graphical estimates. This bound allows to prove regularity and decay properties of the averaged Green's functions and the density of states for a three dimensional model with a thin conducting band and an energy close to the border of the band, for sufficiently small coupling constant.
Magnen Jacques
Poirot Gilles
Rivasseau Vincent
No associations
LandOfFree
The Anderson Model as a Matrix Model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Anderson Model as a Matrix Model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Anderson Model as a Matrix Model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-175895