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This research aims to classify the rigidity of algebraic structures in two-projection quantum Markov semigroups.

May 8, 2026Open Access

Factor Rigidity, Spectral Collapse, and A Maximal Gauge Algebra Pattern in Primitive Two-Projection GKSL Systems

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This research aims to classify the rigidity of algebraic structures in two-projection quantum Markov semigroups.
Developed rigidity classification using Halmos decomposition in separable Hilbert spaces.
Analyzed invariant irreducible subspaces under dynamical constraints, proving finiteness in dimensions 2 and 3.
Introduced factor rigidity index to distinguish phases in three-dimensional dynamics.
For dimension 2, the dynamics closes as factor M_2(C), indicating stability.
In dimension 3, irreducible closure transitions to M_3(C) via Burnside’s theorem, showing dynamical richness.
Identified universal rigidity threshold at n=3 with unique maximal gauge Lie algebra pattern (su(3) ⊕ su(2) ⊕ u(1)).

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Randomized trial assesses maximal gauge algebra patterns in finite-dimensional quantum dynamics, indicating universal rigidity thresholds.

GUANHUA YU (2026) studied this question.

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Randomized trial assesses maximal gauge algebra patterns in finite-dimensional quantum dynamics, indicating universal rigidity thresholds.