Universal Correlations of Coulomb Blockade Conductance Peaks and the Rotation Scaling in Quantum Dots

We show that the parametric correlations of the conductance peak amplitudes of a chaotic or weakly disordered quantum dot in the Coulomb blockade regime become universal upon an appropriate scaling of the parameter. We compute the universal forms of this correlator for both cases of conserved and broken time reversal symmetry. For a symmetric dot the correlator is independent of the details in each lead such as the number of channels and their correlation. We derive a new scaling, which we call the rotation scaling, that can be computed directly from the dot's eigenfunction rotation rate or alternatively from the conductance peak heights, and therefore does not require knowledge of the spectrum of the dot. The relation of the rotation scaling to the level velocity scaling is discussed. The exact analytic form of the conductance peak correlator is derived at short distances. We also calculate the universal distributions of the average level width velocity for various values of the scaled parameter. The universality is illustrated in an Anderson model of a disordered dot.Comment: 35 pages, RevTex, 6 Postscript figure

Symmetry of disciform scars in bilateral age-related macular degeneration.

The size of the final macular scar in subretinal neovascularisation (SRNV) is one of the most important determinants of final visual function in patients with subfoveal disease. We studied patients with bilateral macular scars from age-related subretinal neovascular membranes retrospectively in order to determine whether or not fellow eyes behave similarly. We found a significant correlation between eyes in terms of final scar size (r = 0.50, p less than 0.01). We found that 50% of fellow eyes with large macular scars (greater than 3 x 10(6) microns2) had similar sized lesions, while only 16% of fellow eyes with small macular scars (less than 0.5 x 10(6) microns2) had large scars (p less than 0.01). We discuss the significance of these findings in relation to the pathogenesis of subretinal neovascular membranes, and their implications for treatment