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arXiv · 2602.07887

Quantum Evolution of Hopf Algebra Hamiltonians

Michele Arzano·Antonio Del Prete·Domenico Frattulillo
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Abstract

In recent years, growing attention has been devoted to the possibility that theories with deformed symmetries, associated with certain models of non-commutative spacetime, may encode a fundamental form of decoherence. This effect should be described by a Lindblad-like evolution governed by the non-trivial Hopf algebra structure of the time-evolution generators. In this work we provide a detailed analysis of such possibility for similar Hopf algebra deformations of the Hamiltonian of a qubit. Starting from a critical examination of the very definition of time evolution through the generalized adjoint action, we explore whether a coherent and physically viable framework can be established. In particular, our analysis shows that a more general combination of adjoint actions always guarantees a von Neumann dynamics and, also in the case of deformed spacetime symmetries considered in the literature, a physically viable Lindblad evolution cannot be established.

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Michele Arzano, Antonio Del Prete, Domenico Frattulillo. 2026-02-08. Quantum Evolution of Hopf Algebra Hamiltonians. https://arxiv.org/abs/2602.07887

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