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    "summary": "Aharonov and Anandan defined a geometric phase for a cyclic pure-state evolution by removing the dynamical phase, identifying its holonomy on the space of Hilbert-space rays without an adiabatic requirement.\n\nA quantum state can return to the same physical ray while its state vector acquires a phase. Some of that phase comes from the energy accumulated along the evolution. This paper separates the remainder as a geometric property of the oriented closed ray path. The state need not follow an instantaneous energy eigenstate, so the construction extends beyond Berry’s adiabatic setting. A precessing two-state example connects this phase with a solid angle. The independence claim keeps the ray path fixed; changing the Hamiltonian can still change the path and therefore its phase. The electromagnetic extension chooses reference paths, and its Aharonov–Bohm application is explicitly approximate. These qualifications belong to the result rather than being details left for the reader to reconstruct.",
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        "description": "The construction concerns normalized cyclic pure states returning to the same ray. The geometric phase, modulo 2 pi, depends on the oriented ray loop after removal of the dynamical phase; changing the loop can change it. The Berry limit needs its adiabatic/eigenstate assumptions. The electromagnetic application adds a specified reference-path construction and is approximate. Open paths, mixed states, noise and direct experimental confirmation are outside this target. A later published criticism has not been fully assessed here.",
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      "statement": "# Aharonov and Anandan: geometric phase beyond adiabatic cyclic evolution\n\nAharonov and Anandan defined a geometric phase for a cyclic pure-state evolution by removing the dynamical phase, identifying its holonomy on the space of Hilbert-space rays without an adiabatic requirement.\n\nA quantum state can return to the same physical ray while its state vector acquires a phase. Some of that phase comes from the energy accumulated along the evolution. This paper separates the remainder as a geometric property of the oriented closed ray path. The state need not follow an instantaneous energy eigenstate, so the construction extends beyond Berry’s adiabatic setting. A precessing two-state example connects this phase with a solid angle. The independence claim keeps the ray path fixed; changing the Hamiltonian can still change the path and therefore its phase. The electromagnetic extension chooses reference paths, and its Aharonov–Bohm application is explicitly approximate. These qualifications belong to the result rather than being details left for the reader to reconstruct.\n\n## Scientific scope\n\nThe construction concerns normalized cyclic pure states returning to the same ray. The geometric phase, modulo 2 pi, depends on the oriented ray loop after removal of the dynamical phase; changing the loop can change it. The Berry limit needs its adiabatic/eigenstate assumptions. The electromagnetic application adds a specified reference-path construction and is approximate. Open paths, mixed states, noise and direct experimental confirmation are outside this target. A later published criticism has not been fully assessed here.\n\n## People and systems\n\nY. Aharonov; J. Anandan\n\n\n\n## Original sources\n\n- [Aharonov and Anandan: geometric phase beyond adiabatic cyclic evolution — original scientific article](https://www.tau.ac.il/~yakir/yahp/yh86)\n- [Aharonov and Anandan: geometric phase beyond adiabatic cyclic evolution — publisher deposit](https://api.crossref.org/works/10.1103%2FPhysRevLett.58.1593)\n",
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