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.
Brownian motion is ballistic on short time scales and diffusive on long time scales. Our theoretical investigations indicate that one can observe the exact opposite---an ``anomalous diffusion process'' where initially diffusive motion becomes ballistic on longer time scales---in an ultracold atomic system with a size comparable to macromolecules. This system is the center-of-mass motion of a quantum matter-wave bright soliton for which the dominant source of decoherence is three-particle losses. Our simulations show that such unusual center-of-mass dynamics should be observable on experimentally accessible time scales.
By modelling quantum systems as emerging from a (classical) sub-quantum thermodynamics, the quantum mechanical decay of the wave is shown to simply result from sub-quantum diffusion with a specific diffusion coefficient varying in time due to a particle's changing thermal environment. It is thereby proven that free quantum motion strictly equals ballistic diffusion. The exact quantum mechanical trajectory distributions and the velocity field of the Gaussian wave packet are thus derived solely from classical physics. Moreover, also quantum motion in a linear (e.g., gravitational) potential is shown to equal said ballistic diffusion. Quantitative statements on the trajectories' characteristic behaviours are obtained which provide a detailed micro-causal explanation in full accordance with momentum conservation.