Particle injection into a chain: decoherence versus relaxation for Hermitian and non‐Hermitian dynamics

A model system for the injection of fermionic particles from filled source sites into an empty chain is investigated. The ensuing dynamics for Hermitian as well as for non‐Hermitian time evolution, where the particles cannot return to the bath sites (quantum ratchet), is studied. A non‐homogeneous hybridization between bath and chain sites permits transient currents in the chain. Non‐interacting particles show decoherence in the thermodynamic limit: the average particle number and the average current density in the chain become stationary for long times, whereas the single‐particle density matrix displays large fluctuations around its mean value. Using the numerical time‐dependent density‐matrix renormalization group (t‐DMRG) method it is demonstrated, on the other hand, that sizable density‐density interactions between the particles introduce relaxation which is by orders of magnitudes faster than the decoherence processes.