Equations of motion approach to decoherence and current noise in ballistic interferometers coupled to a quantum bath

We present a technique for treating many particles moving inside a ballistic interferometer, under the influence of a quantum-mechanical environment (phonons, photons, Nyquist noise, etc.). Our approach is based on solving the coupled Heisenberg equations of motion of the many-particle system and the bath, and it is inspired by the quantum Langevin method known for the Caldeira-Leggett model. As a first application, we treat a fermionic Mach-Zehnder interferometer. In particular, we discuss the dephasing rate and present full analytical expressions for the leading corrections to the current noise, brought about by the coupling to the quantum bath. In contrast to a single-particle model, both the Pauli principle as well as the contribution of hole-scattering processes become important, and are automatically taken into account in this method.