Classification of topological phases of matter in stochastic systems
Abstract
Topological phases of matter support edge states protected from random perturbations, and the identification of the discrete non-spatial symmetries and dimensions that support such phases was systematically developed for quantum systems and analogous platforms. While topological phases were also discovered in stochastic systems and posited as mechanisms for key biochemical processes, a classification consistent with their Markovian constraints remains lacking, impeding generalization to new scenarios. To address this, we develop new methods including a new homotopy approach, real-space invariants and a redefinition of the point gap to classify both transient and steady states. We find robust transient states in two symmetry classes, no symmetry and pseudo-Hermiticity respectively, while topological steady states are expected only in systems without symmetry. We identify the dimensions with non-trivial phases and their group structure, creating a rigorous framework for predicting robust behavior in active and living matter.
Related
- Topological phases of bosons with local parity coupling on a dimerized lattice
- Observation of topological Berry phases with a single phonon in an ion microtrap array
- Topological Superconducting Phases in a Strained Altermagnet-Superconductor Heterostructure
- Symmetry-permuting entanglers for non-invertible symmetry-protected topological phases
- Gauging on the lattice and gapped/gapless topological phases
BibTeX
@misc{li2026classification,
title = {{Classification of topological phases of matter in stochastic systems}},
author = {Dexin Li and Evelyn Tang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.38171},
eprint = {2609.38171},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38171},
}
RIS
TY - UNPB
TI - Classification of topological phases of matter in stochastic systems
AU - Dexin Li
AU - Evelyn Tang
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2609.38171
UR - https://arxiv.org/abs/2609.38171
AB - Topological phases of matter support edge states protected from random perturbations, and the identification of the discrete non-spatial symmetries and dimensions that support such phases was systematically developed for quantum systems and analogous platforms. While topological phases were also discovered in stochastic systems and posited as mechanisms for key biochemical processes, a classification consistent with their Markovian constraints remains lacking, impeding generalization to new scenarios. To address this, we develop new methods including a new homotopy approach, real-space invariants and a redefinition of the point gap to classify both transient and steady states. We find robust transient states in two symmetry classes, no symmetry and pseudo-Hermiticity respectively, while topological steady states are expected only in systems without symmetry. We identify the dimensions with non-trivial phases and their group structure, creating a rigorous framework for predicting robust behavior in active and living matter.
ER -