DISTRIBUTION OF PARAMETRIC CONDUCTANCE DERIVATIVES OF A QUANTUM-DOT

The conductance G of a quantum dot with single-mode ballistic point co ntacts depends sensitively on external parameters X, such as gate volt age and magnetic field. We calculate the joint distribution of G and d G/dX by relating it to the distribution of the Wigner-Smith time-delay matrix of a chaotic system. The distribution of dG/dX has a singulari ty zero and algebraic tails. While G and dG/dX are correlated, the rat io of dG/dX and root G(1 - G) is independent of G. Coulomb interaction s change the distribution of dG/dX, by inducing a transition from the grand-canonical to the canonical ensemble. All these predictions can b e tested in semiconductor microstructures or microwave cavities.