Quantum transport: A unified approach via a multivariate hypergeometric generating function

Abstract

We introduce a characteristic function method to describe charge-counting statistics (CCS) in phase coherent systems that directly connects the three most successful approaches to quantum transport: random-matrix theory (RMT), the nonlinear σ-model and the trajectory-based semiclassical method. The central idea is the construction of a generating function based on a multivariate hypergeometric function, which can be naturally represented in terms of quantities that are well-defined in each approach. We illustrate the power of our scheme by obtaining exact analytical results for the first four cumulants of CCS in a chaotic quantum dot coupled ideally to electron reservoirs via perfectly conducting leads with arbitrary number of open scattering channels.