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• W2896580189 abstract "Linear Hamiltonian systems with time-dependent coefficients are of importance to nonlinear Hamiltonian systems, accelerator physics, plasma physics, and quantum physics. It is shown that the solution map of a linear Hamiltonian system with time-dependent coefficients can be parameterized by an envelope matrix w(t), which has a clear physical meaning and satisfies a nonlinear envelope matrix equation. It is proved that a linear Hamiltonian system with periodic coefficients is stable if and only if the envelope matrix equation admits a solution with periodic w†w and a suitable initial condition. The mathematical devices utilized in this theoretical development with significant physical implications are time-dependent canonical transformations, normal forms for stable symplectic matrices, and horizontal polar decomposition of symplectic matrices. These tools systematically decompose the dynamics of linear Hamiltonian systems with time-dependent coefficients and are expected to be effective in other studies as well, such as those on quantum algorithms for classical Hamiltonian systems." @default.
• W2896580189 created "2018-10-26" @default.
• W2896580189 creator A5007354836 @default.
• W2896580189 date "2019-02-01" @default.
• W2896580189 modified "2023-09-23" @default.
• W2896580189 title "A necessary and sufficient condition for the stability of linear Hamiltonian systems with periodic coefficients" @default.
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• W2896580189 doi "https://doi.org/10.1063/1.5067391" @default.
• W2896580189 hasPublicationYear "2019" @default.
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