Transport in open quantum systems in presence of lossy channels

TL;DR

This paper investigates how different configurations of particle loss affect transport properties in a one-dimensional fermionic lattice, revealing conditions under which conductance remains robust or becomes anomalous or ballistic.

Contribution

It introduces a detailed analysis of conductance scaling in open quantum systems with various loss configurations, linking spectral properties to transport behavior.

Findings

Conductance remains robust for certain loss configurations within and outside the band.

Anomalous conductance scaling occurs at the band edge due to spectral properties.

Extensive loss channels lead to ballistic conductance in the thermodynamic limit.

Abstract

We study nonequilibrium steady state (NESS) transport in a boundary driven one-dimensional fermionic lattice setup which is further subjected to particle loss. We analyze the system size scaling of conductance at zero temperature for different values of the chemical potential of the boundary reservoirs. We consider a variety of loss channel configurations: (i) single loss at the middle site of the lattice, (ii) multiple but nonextensive lossy channels, and (iii) extensive lossy channels. For the cases (i) and (ii), the conductance scaling with system size remains robust (i.e., same as the case with no loss) for chemical potential within and outside the lattice band, while at the band-edge rich anomalous conductance scaling emerges. For case (iii), the conductance scaling becomes ballistic in the thermodynamic limit for any value of chemical potential. We explain the emergence of these different system size scalings of conductance by analyzing the spectral properties of the associated non-hermitian transfer matrices of the underlying lattice. We demonstrate that the emergence of anomalous scaling is deeply connected to the existence of exceptional points of transfer matrices. Our study unravels that by carefully optimizing the loss mechanism configurations, one can in principle realize systems with rich transport properties in low-dimensional open quantum systems.