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Non-Hermitian topology for stochastic systems and relevant symmetries

Establish the relationship between non-Hermitian topological classifications and master-equation-based stochastic systems, and identify the symmetry classes that are relevant for biological networks.

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Background

Topological classifications originating from random matrix theory are well developed for Hermitian systems, and recent work has begun extending them to non-Hermitian settings.

Stochastic systems mapped from master equations are inherently non-Hermitian for exhibiting edge states, but a dedicated classification that directly captures their topological phases and the relevant symmetries for biological applications remains to be established.

References

While some topological classifications of non-Hermitian Hamiltonians have been recently proposed , the relation of non-Hermitian topology to stochastic systems and the relevant symmetries for biological systems are questions that remain open.

— Topological phases in discrete stochastic systems (2406.03925 - Agudo-Canalejo et al., 6 Jun 2024) in Section 6.5 (Topological classification using symmetries)