Time-resolved topology of aperiodically driven systems

Abstract

Topological phases of periodically driven systems are commonly classified through Floquet Hamiltonians, whose definition relies on a repeated driving cycle. However, this framework breaks down for systems whose realized evolution is aperiodic or nonlinear, even when robust topological phenomena appear to persist. Here, we introduce an evolution-history spectral localizer framework that classifies Chern topology directly from a system's finite-time unitary evolution operator. The method produces a time-resolved local Chern marker and an associated local gap, allowing topology and its protection to be tracked during the actual dynamics of a driven system. We demonstrate this approach in quasiperiodically driven and nonlinear photonic models, where it identifies transient topological protection, its subsequent loss, and the recovery of topology after nonlinear excitations disperse. The developed framework provides a route for analyzing driven photonic systems whose topological behavior depends on finite-time dynamics rather than an idealized Floquet cycle.

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BibTeX RIS

BibTeX

@misc{cole2026timeresolved,
  title = {{Time-resolved topology of aperiodically driven systems}},
  author = {Justin T. Cole and Christina Jörg and Terry A. Loring and Alexander Cerjan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19348},
  eprint = {2609.19348},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19348},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Time-resolved topology of aperiodically driven systems
AU  - Justin T. Cole
AU  - Christina Jörg
AU  - Terry A. Loring
AU  - Alexander Cerjan
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.19348
UR  - https://arxiv.org/abs/2609.19348
AB  - Topological phases of periodically driven systems are commonly classified through Floquet Hamiltonians, whose definition relies on a repeated driving cycle. However, this framework breaks down for systems whose realized evolution is aperiodic or nonlinear, even when robust topological phenomena appear to persist. Here, we introduce an evolution-history spectral localizer framework that classifies Chern topology directly from a system's finite-time unitary evolution operator. The method produces a time-resolved local Chern marker and an associated local gap, allowing topology and its protection to be tracked during the actual dynamics of a driven system. We demonstrate this approach in quasiperiodically driven and nonlinear photonic models, where it identifies transient topological protection, its subsequent loss, and the recovery of topology after nonlinear excitations disperse. The developed framework provides a route for analyzing driven photonic systems whose topological behavior depends on finite-time dynamics rather than an idealized Floquet cycle.
ER  -

Abstract

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