Single level current and curvature distributions in mesoscopic systems

Alex Kamenev; Daniel Braun

doi:doi:10.1051/jp1:1994183

Numéro		J. Phys. I France Volume 4, Numéro 7, July 1994


Page(s)		1049 - 1062
DOI		https://doi.org/10.1051/jp1:1994183

DOI: 10.1051/jp1:1994183
J. Phys. I France 4 (1994) 1049-1062

Single level current and curvature distributions in mesoscopic systems

Alex Kamenev¹ and Daniel Braun²

¹ Department of Nuclear Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
² Laboratoire de Physique des Solides, Bat 510, Université Paris-Sud, 91405 Orsay, France

(Received 26 October 1993, accepted 16 March 1994)

Abstract
Exact analytic results for single level current and curvature distribution functions are derived within the framework of a $2\times 2$ random matrix model. Current and curvature are defined as the first and second derivatives of energy with respect to a time-reversal symmetry breaking parameter (magnetic flux). The applicability of the obtained distributions for the spectral statistic of disordered metals is discussed. The most surprising feature of our results is the divergence of the second and higher moments of the curvature at zero flux. It is shown that this divergence also appears in the general $N\times N$ random matrix model. Furthermore, we find an unusual logarithmic behavior of the two point current-current correlation function at small flux.