Fanchiotti, H., Garcia Canal, C. A., Mayosky, M., Veiga, A., & Vento, V. (2023). The Geometric Phase in Classical Systems and in the Equivalent Quantum Hermitian and Non-Hermitian PT-Symmetric Systems. Braz. J. Phys., 53(6), 143–11pp.
Abstract: The decomplexification procedure allows one to show mathematically (stricto sensu) the equivalence (isomorphism) between the quantum dynamics of a system with a finite number of basis states and a classical dynamics system. This unique way of connecting different dynamics was used in the past to analyze the relationship between the well-known geometric phase present in the quantum evolution discovered by Berry and its generalizations, with their analogs, the Hannay phases, in the classical domain. In here, this analysis is carried out for several quantum hermitian and non-hermitian PT-symmetric Hamiltonians and compared with the Hannay phase analysis in their classical isomorphic equivalent systems. As the equivalence ends in the classical domain with oscillator dynamics, we exploit the analogy to propose resonant electric circuits coupled with a gyrator, to reproduce the geometric phase coming from the theoretical solutions, in simulated laboratory experiments.
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Fanchiotti, H., Garcia Canal, C. A., Mayosky, M., Veiga, A., & Vento, V. (2022). Measuring the Hannay geometric phase. Am. J. Phys., 90(6), 430–435.
Abstract: The Hannay geometric phase is the classical analog of the well-known Berry phase. Its most familiar example is the effect of the latitude lambda on the motion of a Foucault pendulum. We describe an electronic network whose behavior is exactly equivalent to that of the pendulum. The circuit can be constructed from off-the-shelf components using two matched transconductance amplifiers that comprise a gyrator to introduce the non-reciprocal behavior needed to mimic the pendulum. One may precisely measure the dependence of the Hannay phase on lambda by circuit simulation and by laboratory measurements on a constructed circuit.
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