Abstract
We study the effect of left-right symmetry on the distribution of the parametric derivative of the dimensionless conductance T with respect to an external parameter X , partial differentialT/ partial differentialX , of ballistic chaotic cavities with two leads, each supporting N propagating modes. We show that T and partial differentialT/ partial differentialX are linearly uncorrelated for any N . For N=1 we calculate the distribution of partial differentialT/ partial differentialX in the presence and absence of time-reversal invariance. In both cases, it has a logarithmic singularity at zero derivative and algebraic tails with an exponent different from the one of the asymmetric case. We also obtain explicit analytical results for the mean and variance of the distribution of partial differentialT/ partial differentialX for arbitrary N . Numerical simulations are performed for N=5 and 10 to show that the distribution P ( partial differentialT/ partial differentialX) tends towards a Gaussian one when N increases.
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