Single Level Current and Curvature Distributions in Mesoscopic Systems

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.