# Dynamical signatures of topological order in the driven-dissipative Kitaev chain

## TL;DR

This paper introduces a method to identify dynamical signatures of topological order in open quantum systems, specifically in a driven-dissipative Kitaev chain, by analyzing bulk winding numbers and edge modes.

## Contribution

It proposes a novel approach to classify topological phases in dissipative systems through dynamical signatures and links these to observable edge modes and currents.

## Key findings

- Bulk winding numbers relate to Majorana edge modes.
- Dissipation causes decay but preserves dynamical topological signatures.
- Periodic driving reveals higher winding numbers and new edge modes.

## Abstract

We investigate the effects of dissipation and driving on topological order in superconducting nanowires. Rather than studying the non-equilibrium steady state, we propose a method to classify and detect dynamical signatures of topological order in open quantum systems. Bulk winding numbers for the Lindblad generator $\hat{\mathcal{L}}$ of the dissipative Kitaev chain are found to be linked to the presence of Majorana edge master modes -- localized eigenmodes of $\hat{\mathcal{L}}$. Despite decaying in time, these modes provide dynamical fingerprints of the topological phases of the closed system, which are now separated by intermediate regions where winding numbers are ill-defined and the bulk-boundary correspondence breaks down. Combining these techniques with the Floquet formalism reveals higher winding numbers and different types of edge modes under periodic driving. Finally, we link the presence of edge modes to a steady state current.