Quantum Evolution of Hopf Algebra Hamiltonians

• URL: http://arxiv.org/abs/2602.07887v1
• Date: Sun, 08 Feb 2026 09:37:59 GMT
• Title: Quantum Evolution of Hopf Algebra Hamiltonians
• Authors: Michele Arzano, Antonio Del Prete, Domenico Frattulillo,
• Abstract summary: Deformed spacetime symmetries may encode a fundamental form of decoherence.<n>This effect should be described by a Lindblad-like evolution governed by the non-trivial Hopf algebra structure of the time-evolution generators.<n>In particular, our analysis shows that a more general combination of adjoint actions always guarantees a von Neumann dynamics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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