Distribution of charge cumulants of a chaotic quantum dot with nonideal contacts

Abstract

We performed numerical simulations of a quantum dot with nonideal contacts to obtain the probability distributions of transport observables associated with the first four charge-transfer cumulants (CTCs). For particular cases, several known results of the recent literature were recovered from our simulations, such as CTC distributions for systems with ideal contacts and CTC distributions for single-channel systems with contacts of arbitrary transparency. We analyze how CTC distributions are affected by a change in the number of open scattering channels in the leads and in the transparencies of the contacts. We found two remarkable features in the CTC distributions in the extreme quantum limit of a small number of open channels: an approximate similarity law for conductance distributions and the appearance of nonanalyticities in some CTC distributions. We interpret the appearance of these singularities by means of a geometrical argument and derive the exact values of the CTC at which the nonanalyticities in the corresponding distribution appear. Our simulations were performed via three different and independent algorithms, whose relative efficiencies are duly compared.