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

TL;DR

This paper explores how fermionic particles injected into a chain exhibit decoherence and relaxation under Hermitian and non-Hermitian dynamics, revealing the impact of interactions on relaxation times.

Contribution

It introduces a model for particle injection into a chain and compares decoherence and relaxation processes under different dynamics, highlighting the role of interactions.

Findings

Decoherence leads to stationary average particle number and current in the thermodynamic limit.

Interactions significantly accelerate relaxation compared to decoherence.

Non-Hermitian dynamics prevent particle return, affecting current flow.

Abstract

We investigate a model system for the injection of fermionic particles from filled source sites into an empty chain. We study the ensuing dynamics for Hermitian as well as for non-Hermitian time evolution where the particles cannot return to the bath sites (quantum ratchet). 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 we demonstrate, 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.