A hypergeometric generating function approach to charge counting statistics in ballistic chaotic cavities

We apply the method of multivariate hypergeometric generating function to study cumulants of the charge counting statistics (CCS) of a ballistic chaotic cavity coupled ideally to two electron reservoirs via perfect conducting leads with an arbitrary number of scattering channels. The underlying chaotic dynamics causes each cumulant of CCS, denoted charge transfer cumulant (CTC), to behave like a random variable, which we describe via exact calculations of its statistical moments and cumulants. Besides reproducing several known results of the literature for the first few statistical cumulants of conductance and shot-noise power, which are the first and second CTC respectively, we obtain new exact results for the first four statistical cumulants of the third and fourth CTC. All analytical results are supported by numerical simulations of the circular ensembles.