Adiabatic driving and geometric phases in classical systems

• URL: http://arxiv.org/abs/2305.14511v1
• Date: Tue, 23 May 2023 20:32:57 GMT
• Title: Adiabatic driving and geometric phases in classical systems
• Abstract summary: We study the concepts of adiabatic driving and geometric phases of classical integrable systems under the Koopman-von Neumann formalism. We use quantum formulas to write a classical adiabatic gauge potential that generates adiabatic unitary flow between classical eigenstates.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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