# Topology by Dissipation: Majorana Bosons in Metastable Quadratic Markovian Dynamics

**Authors:** Vincent P. Flynn, Emilio Cobanera, Lorenza Viola  
**arXiv:** [2104.03985](https://arxiv.org/abs/2104.03985)  
**Date:** 2021-04-08  
**Summary page:** https://www.summarizepaper.com/en/paper/2104.03985v2/

## Key points

- Majorana bosons are tight bosonic analogs of the Majorana fermionic quasiparticles in condensed matter physics
- Their emergence was considered impossible for gapped free bosonic matter within a standard Hamiltonian scenario
- Recent research has shown that their emergence is possible in noninteracting bosonic chains undergoing Markovian dissipation
- This leads to a distinctive form of topological metastability where a conserved Majorana boson localized on one edge is paired with a symmetry generator localized on the opposite edge
- Majorana bosons are robust against disorder and identifiable by signatures in the zero-frequency steady-state power spectrum
- Symmetry-protected topological phases for free bosons may arise in transient metastable regimes, which persist over practical timescales
- Understanding Liouvillian exceptional points is crucial in determining the stability and dynamics of these systems
- Kitaev's work on unpaired Majorana fermions in quantum wires and Teo and Kane's proposal for topological insulators with gapless surface states protected by time-reversal symmetry are referenced
- This research sheds light on new possibilities for understanding topological phases in open quantum systems and provides insight into how they may be experimentally observed through their distinct spectral signatures.

## Summary

. The emergence of Majorana bosons, which are tight bosonic analogs of the Majorana fermionic quasiparticles in condensed matter physics, has been considered impossible for gapped free bosonic matter within a standard Hamiltonian scenario. However, recent research has shown that the interplay between dynamical metastability and nontrivial bulk topology can make their emergence possible in noninteracting bosonic chains undergoing Markovian dissipation. This leads to a distinctive form of topological metastability where a conserved Majorana boson localized on one edge is paired with a symmetry generator localized on the opposite edge. The study argues that Majorana bosons are robust against disorder and identifiable by signatures in the zero-frequency steady-state power spectrum. This research suggests that symmetry-protected topological phases for free bosons may arise in transient metastable regimes, which persist over practical timescales. The study also highlights the importance of understanding Liouvillian exceptional points, which are singularities in the spectrum of the Liouvillian superoperator governing open quantum systems, as they play a crucial role in determining the stability and dynamics of these systems. Additionally, it references Kitaev's work on unpaired Majorana fermions in quantum wires and Teo and Kane's proposal for topological insulators with gapless surface states protected by time-reversal symmetry. Overall, this research sheds light on new possibilities for understanding topological phases in open quantum systems and provides insight into how they may be experimentally observed through their distinct spectral signatures.