Single Level Current and Curvature Distributions in Mesoscopic Systems

TL;DR

This paper derives exact analytical distributions for single level current and curvature in mesoscopic systems using a 2x2 random matrix model, revealing divergences at zero flux and unusual correlation behaviors.

Contribution

It provides the first exact analytic expressions for current and curvature distributions in mesoscopic systems within a random matrix framework, highlighting divergence phenomena.

Findings

Curvature moments diverge at zero flux.

Logarithmic behavior of current-current correlation at small flux.

Distributions applicable to disordered metals' spectral statistics.

Abstract

Exact analytic results for single level current and curvature distribution functions are derived in a 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.