Fermions on a 1D lattice: localized sources and sinks with dephasing

Abstract

We study a general one-dimensional spinless fermionic system subject to a localized source, sink, and bulk dephasing. Within the Lindblad framework, we compute the time evolution of the density profile and spatial correlation functions. We find that the presence of bulk dephasing suppresses certain coherent quantum features, such as the Friedel oscillations, and it alters the transport dynamics to exhibit two distinct dynamical regimes instead of three as observed in the absence of dephasing. This effect can be understood as the destruction of ballistic motion caused by the dephasing noise. Under strong dephasing, the density profile becomes similar to the one expected for a classical diffusive regime. We also investigate the system in the presence of both a localized source and sink, placed at a distance of $\Delta$. Interestingly, quantum coherence generates secondary density peaks at integer multiples of the source-sink separation $\Delta$, which are systematically washed out as bulk dephasing drives the system toward the classical diffusive limit.