# Relation between the Berry phase in quantum hermitian and non-hermitian systems and the Hannay phase in the equivalent classical systems

@inproceedings{Fanchiotti2022RelationBT, title={Relation between the Berry phase in quantum hermitian and non-hermitian systems and the Hannay phase in the equivalent classical systems}, author={H. Fanchiotti and C. A. Garc{\'i}a Canal and Miguel Angel Mayosky and A. Veiga and Vicente Vento}, year={2022} }

The well-known geometric phase present in the quantum adiabatic evolution discovered by Berry many years ago has its analogue, the Hannay phase, in the classical domain. We calculate the Berry phase with examples for quantum hermitian and non-hermitian PT -symmetric Hamiltonians and compare with the Hannay phase in their classical equivalents. We use the analogy to propose resonant electric circuits which reproduce the theoretical solutions in simulated laboratory experiments.

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