Inelastic interaction corrections and universal relations for full counting statistics in a quantum contact

We analyze in detail the interaction correction to full counting statistics (FCS) of electron transfer in a quantum contact originating from the electromagnetic environment surrounding the contact. The correction can be presented as a sum of two terms, corresponding to elastic-inelastic electron transfer. Here we primarily focus on the inelastic correction. For our analysis, it is important to understand more general-universal-relations imposed on FCS only by quantum mechanics and statistics with no regard for a concrete realization of a contact. So we derive and analyze these relations. We reveal that for FCS the universal relations can be presented in a form of detailed balance. We also present several useful formulas for the cumulants. To facilitate the experimental observation of the effect, we evaluate cumulants of FCS at finite voltage and temperature. Several analytical results obtained are supplemented by numerical calculations for the first three cumulants at various transmission eigenvalues.