TY  - JOUR
AU  - Fanchiotti, H.
AU  - Garcia Canal, C. A.
AU  - Mayosky, M.
AU  - Veiga, A.
AU  - Vento, V.
PY  - 2023
DA  - 2023//
TI  - The Geometric Phase in Classical Systems and in the Equivalent Quantum Hermitian and Non-Hermitian PT-Symmetric Systems
T2  - Braz. J. Phys.
JO  - Brazilian Journal of Physics
SP  - 143 - 11pp
VL  - 53
IS  - 6
PB  - Springer
KW  - Geometrical phases
KW  - Decomplexification
KW  - Resonat circuit
KW  - Gyrator
AB  - 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.
SN  - 0103-9733
UR  - https://doi.org/10.1007/s13538-023-01350-5
DO  - 10.1007/s13538-023-01350-5
LA  - English
N1  - WOS:001058597300001
ID  - Fanchiotti_etal2023
ER  -