Helical Quasiperiodic Chains with Engineered Dissipation: Liouvillian Rapidity Diagnostics of Transport and Localization

TL;DR

This paper investigates how engineered dissipation affects relaxation and localization in a quasiperiodic fermionic chain, using Liouvillian rapidities as diagnostics for transport properties.

Contribution

It introduces a detailed analysis of Liouvillian spectra in a helical quasiperiodic chain with various dissipation patterns, linking spectral features to localization and transport.

Findings

Uniform dissipation yields large, weakly lambda-dependent gaps.

Sparse local dissipation causes gaps to shrink with increasing quasiperiodic potential.

Finite-size scaling and spectral statistics connect Liouvillian structure to localization.

Abstract

We study relaxation spectra of a quadratic spinless--fermion helical chain with an Aubry--Andre--type quasiperiodic potential and a single N--th neighbor (helical) hopping. Dissipation and pumping are introduced via local linear Lindblad jump operators and treated exactly using the third--quantization / Majorana covariance formalism. Focusing on periodic boundary conditions (to avoid edge artefacts) we compute the Liouvillian rapidities and their smallest nonzero real part (the rapidity gap) for several spatial dissipation patterns: uniform (all), single--site (one--site) and two--site (two--site) placement, plus pairwise gain/loss on helical partner sites. We show that uniform dissipation yields large, weakly lambda--dependent gaps, while sparse local dissipation produces gaps that shrink rapidly as the quasiperiodic potential lambda induces localization. Increasing t_N enhances relaxation by improving mode overlap with dissipative channels. Finite--size scaling, rapidity level statistics (Poisson vs Wigner--Dyson), and spatial profiles of slow modes provide a consistent picture linking Liouvillian spectral structure to transport and localization. Our results highlight Liouvillian rapidities as compact, experimentally relevant diagnostics of relaxation and sensitivity in engineered open quantum lattices.