Aharonov and Anandan: geometric phase beyond adiabatic cyclic evolution

What changed

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.

Scientific scope

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. 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.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

• Y. Aharonov · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
• J. Anandan · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.

• Aharonov and Anandan: geometric phase beyond adiabatic cyclic evolution — original scientific article
• Aharonov and Anandan: geometric phase beyond adiabatic cyclic evolution — publisher deposit

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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