Symmetry in Full Counting Statistics, Fluctuation Theorem, and Relations among Nonlinear Transport Coefficients in the Presence of a Magnetic Field

We study full counting statistics of coherent electron transport through multi-terminal interacting quantum-dots under a finite magnetic field. Microscopic reversibility leads to the symmetry of the cumulant generating function, which generalizes the fluctuation theorem in the context of quantum transport. Using this symmetry, we derive the Onsager-Casimir relation in the linear transport regime and universal relations among nonlinear transport coefficients.