PhaseGeometry Z₂: Decoherence, Quantum Darwinism and Branching in a Binary Phase Medium

Turchanov, Aleksey

Published Dec 1, 2025• 0 citations

Abstract

This record contains the preprint version of the article “PhaseGeometry Z₂: Decoherence, Quantum Darwinism and Branching in a Binary Phase Medium”, submitted to a peer-reviewed journal. The work develops a unified quantum–foundational layer of the PhaseGeometry Z₂ programme, in which a single real scalar field with a Z₂-symmetric double-well potential plays a dual role:– as a cosmological substrate, whose homogeneous broken phase sources dark-energy–like expansion and whose inhomogeneities generate dark-matter–like halo profiles and static black holes with binary phase hair;– as a quantum phase medium, within which systems, apparatuses, observers and classical branches are all realised as patterns of the same underlying field. On the physical side, the article introduces a finite Z₂ chain evolving under a transverse-field Ising Hamiltonian as a fully explicit “toy Universe” of the phase medium. Within this model it demonstrates, under strictly unitary dynamics:– rapid decoherence of macroscopically distinct binary events;– saturation of the subsystem entropy at classical values;– the emergence of a clear Quantum Darwinism plateau in the mutual information between the system and environment fragments, signalling redundant objective records. On the conceptual side, the work formulates an ontology in which:– observers are stable, information-rich patterns in the phase medium;– branches are identified with disjoint amplitude humps in Z₂ configuration space;– delayed-choice and quantum-eraser scenarios are reinterpreted in a purely unitary, medium-based language. Taken together, these results show that the PhaseGeometry Z₂ phase medium can simultaneously underpin dark-sector phenomenology and the emergence of classical observers and histories, providing a concrete Everett–Zurek–style measurement framework in a closed Universe. A related two-part foundations set (“PhaseGeometry Z₂ Foundations IV–V: Phase medium, observers, decoherence and Quantum Darwinism”, DOI: 10.5281/zenodo.17772072) presents a more modular split between ontology (IV) and numerical implementation (V). This preprint is part of the PhaseGeometry Z₂ Core Package v1.0: “Binary Phase, Dark Energy and Dark Matter” (series DOI: 10.5281/zenodo.17652957). All materials are released under the Creative Commons Attribution 4.0 International (CC BY 4.0) licence.

DOI: 10.5281/zenodo.17773134

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Quantum Darwinism and decoherence show why, in such nonequilibrium multipartite settings, pointer states—and not their superpositions—survive and information about them is amplified and recorded in many copies by the environment. Both the nonequilibrium setting and the division of the universe into systems are needed to state the problem. When certain assumptions are needed to state the problem, surely they can be used to solve it.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. M. Zwolak, W. H. Zurek, Sci. Rep. 3, 1729 (2013); https://doi.org/10.1038/srep01729, Google ScholarCrossrefA. Streltsov, W. H. Zurek, Phys. Rev. Lett. 111, 040401 (2013). https://doi.org/10.1103/PhysRevLett.111.040401, , Google ScholarCrossref2. L. D. Romero, J. P. Paz, Phys. Rev. A 55, 4070 (1997). https://doi.org/10.1103/PhysRevA.55.4070, Google ScholarCrossref3. C. J. Riedel, W. H. Zurek, Phys. Rev. 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