Particle injection into a chain: Decoherence versus relaxation for Hermitian and non-Hermitian dynamics

Abstract

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. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.