Author(s):

Erdős, László; Knowles, Antti

Article Title: 
The AltshulerShklovskii formulas for random band matrices I: the unimodular case

Affiliation 
IST Austria 
Abstract: 
We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We show that the correlation function of the local eigenvalue density exhibits a universal power law behaviour that differs from the WignerDyson Mehta statistics. This law had been predicted in the physics literature by Altshuler and Shklovskii in (Zh Eksp Teor Fiz (Sov Phys JETP) 91(64):220(127), 1986); it describes the correlations of the eigenvalue density in general metallic sampleswith weak disorder. Our result rigorously establishes the AltshulerShklovskii formulas for band matrices. In two dimensions, where the leading term vanishes owing to an algebraic cancellation, we identify the first nonvanishing term and show that it differs substantially from the prediction of Kravtsov and Lerner in (Phys Rev Lett 74:25632566, 1995). The proof is given in the current paper and its companion (Ann. H. Poincaré. arXiv:1309.5107, 2014).

Journal Title:

Communications in Mathematical Physics

Volume: 
333

Issue 
3

ISSN:

14320916

Publisher:

Springer

Date Published:

20150201

Start Page: 
1365

End Page:

1416

Sponsor: 
Partially supported by SFBTR 12 Grant of the German Research Council.

URL: 

DOI: 
10.1007/s0022001421195

Open access: 
yes (repository) 