Statistical properties of one-point Green functions in disordered systems and critical behavior near the Anderson transition

Issue		J. Phys. I France Volume 4, Number 5, May 1994


Page(s)		655 - 673
DOI		10.1051/jp1:1994168

DOI: 10.1051/jp1:1994168
J. Phys. I France 4 (1994) 655-673

Statistical properties of one-point Green functions in disordered systems and critical behavior near the Anderson transition

Alexander D. Mirlin¹ and Yan V. Fyodorov²

¹ Institut für Theorie der Kondensierten Materie, Universitât Karlsruhe, 76128 Karlsruhe, Germany
² Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel

(Received 1 Octoher 1993, accepted 9 Fehruary 1994)

Abstract
We investigate the statistics of local Green functions $G(E, x, x) = \langle x \vert(E - \hat{H})^{-1}\vert x\rangle$ , in particular of the local density of states $\rho \propto Im G(E, x, x)$ , with the Hamiltonian $\hat{H}$ describing the motion of a quantum particle in a d-dimensional disordered system. Corresponding distributions are related to a function which plays the role of an order parameter for the Anderson metal-insulator transition. When the system can be described by a nonlinear $\sigma$ -model, the distribution is shown to possess a specific "inversion" symmetry. We present an analysis of the critical behavior near the mobility edge that follows from the abovementioned relations. We explain the origin of the non-power-like critical behavior obtained earlier for effectively infinite-dimensional models. For any finite dimension $d < \infty$ the critical behavior is demonstraied to be of the conventional power-law type wilh $d = \infty$ playing the rote of an upper critical dimension.

What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.

If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.