Effect of the spatial reflection symmetry on the distribution of the   parametric conductance derivative in ballistic chaotic cavities
  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, dT/dX, of ballistic chaotic cavities with two leads, each supporting N propagating modes. We show that T and dT/dX are uncorrelated for any N. For N=1 we calculate the distribution of dT/dX 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 dT/dX for arbitrary N. Numerical simulations are performed for N=5 and 10 to show that the distribution P(dT/dX) tends towards a Gaussian one when N increases. 
M. Martinez-Mares and E. Castano