Nonlinear Dynamics of Rapidly Driven Systems
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918528318177280 |
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| author | Besharat, Afshin Penin, Alexander A. |
| author_facet | Besharat, Afshin Penin, Alexander A. |
| contents | We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in inverse powers of the oscillation frequency $ω$. The explicit expression for the effective Lagrangian is derived up to ${\cal O}(1/ω^6)$ next-to-next-to-leading approximation. The general structure of the high-frequency expansion reveals a broad class of nonlinear systems whose transition curves are identical to those of the linear Mathieu equation, which enables a fully nonperturbative stability analysis in the case of strong driving and nonlinearity. The method is generalized to velocity-dependent forces and configuration space with curvature, characteristic to systems with constraints. Several applications are discussed in detail, including the dynamical magnetic trapping of electric charges. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_28996 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonlinear Dynamics of Rapidly Driven Systems Besharat, Afshin Penin, Alexander A. Chaotic Dynamics Mesoscale and Nanoscale Physics High Energy Physics - Phenomenology Atomic Physics Classical Physics We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in inverse powers of the oscillation frequency $ω$. The explicit expression for the effective Lagrangian is derived up to ${\cal O}(1/ω^6)$ next-to-next-to-leading approximation. The general structure of the high-frequency expansion reveals a broad class of nonlinear systems whose transition curves are identical to those of the linear Mathieu equation, which enables a fully nonperturbative stability analysis in the case of strong driving and nonlinearity. The method is generalized to velocity-dependent forces and configuration space with curvature, characteristic to systems with constraints. Several applications are discussed in detail, including the dynamical magnetic trapping of electric charges. |
| title | Nonlinear Dynamics of Rapidly Driven Systems |
| topic | Chaotic Dynamics Mesoscale and Nanoscale Physics High Energy Physics - Phenomenology Atomic Physics Classical Physics |
| url | https://arxiv.org/abs/2605.28996 |