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arXiv · 2305.14511

Adiabatic driving and geometric phases in classical systems

A. D. Bermúdez Manjarres
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Abstract

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\left\{ i\Phi\right\} $ after a closed variation of the parameters $\lambda$ in its associated Hamiltonian. The explicit form of $\Phi$ 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.

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A. D. Bermúdez Manjarres. 2023-05-23. Adiabatic driving and geometric phases in classical systems. https://arxiv.org/abs/2305.14511

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