Microreversibility and the statistics of currents in quantum transport

For the statistics of currents in quantum transport, microreversibility is shown to provide a way to obtain the statistical cumulants at the order n+1 from the measurement of the cumulants at the order n or lower. This fundamental result is based on relations generalizing the fluctuation-dissipation theorem and the Onsager-Casimir reciprocal relations from linear toward nonlinear transport properties, as a consequence of the time-reversal symmetry of the underlying microscopic Hamiltonian dynamics. The method is demonstrated in detail in the case of multiterminal Aharonov-Bohm rings. Within the independent electron approximation, the cumulant generating function, which fully specifies the statistics of the nonequilibrium currents, is obtained from the scattering matrix of these circuits. The time-reversal symmetry relations are explicitly shown to express the cumulants at equilibrium up to the fourth order in terms of lower-order cumulants and their nonequilibrium responses in the presence of an external magnetic field.