2023/05/23 by Manjarres, A. D. Bermúdez
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2305.14511
We study the concepts of adiabatic driving and geometric phases of classical integrable systems under the Koopman-von Neumann formalism. In close relation to what happens to a quantum state, a classical Koopman-von Neumann eigenstate will acquire a geometric phase factor exp\ iΦ\ after a closed variation of the parameters λ in its associated Hamiltonian. The explicit form of Φ is then derived for integrable systems, and its relation with the Hannay angles is shown. Additionally, we use quantum formulas to write a classical adiabatic gauge potential that generates adiabatic unitary flow between classical eigenstates, and we explicitly show the relationship between the potential and the classical geometric phase.