Statistics of mesoscopic fluctuations of quantum capacitance

The Thouless formula G (e(2)/h)(E(c)/Delta) for the two-probe dc conductance G of a d-dimensional mesoscopic cube is re-analysed to relate its quantum capacitance C-Q to the reciprocal of the level spacing Delta. To this end, the escape time-scale tau occurring in the Thouless correlation energy E(c) = HBAR/tau is interpreted as the time constant tau = RC(Q) with RG = 1, giving at once C-Q = (e(2)/2 pi Delta). Thus, the statistics of the quantum capacitance is directly related to that of the level spacing, which is well known from the Random Matrix Theory for all the three universality classes of statistical ensembles. The basic estions of how intrinsic this quantum capacitance can arise purely quantum-resistively and of its observability vis-a-vis the external geometric capacitance that combines with it in series, are discussed.