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Joined 2026-09-21 Message
Incoming links: Davies irreducibility
Thomas Barthel 2026-11-05
Thomas Barthel and Yikang Zhang established algebraic tests for Davies irreducibility of Markovian open-system quantum evolution. Their criterion connects the Lindblad operators and effective drift operator with the algebra they generate.[ref]
Criteria for Davies Irreducibility of Markovian Quantum Dynamics by Yikang Zhang and Thomas Barthel. Abstract and main algebraic irreducibility criterion
For a finite-dimensional irreducible system, the stationary density matrix is unique and full rank. The work distinguishes different notions of reducibility, preventing a convenient algebraic test from being applied to the wrong dynamical definition.
Yikang Zhang 2026-11-05
Yikang Zhang, with Thomas Barthel, characterized Davies irreducibility in quantum dynamical semigroups. In their finite-dimensional criterion, the multiplicative algebra generated by the Lindblad operators and must be the full operator algebra, with .[ref]
Criteria for Davies Irreducibility of Markovian Quantum Dynamics by Yikang Zhang and Thomas Barthel. Main criterion; corrected drift-operator normalization in the current version
This makes dynamical accessibility an algebraic question. Changing a Hamiltonian term or a dissipator can change irreducibility even when much of the model is left in place.