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Floquet Theory and Newton’s Method
Journal of Applied Mechanics, 1973Application of Newton’s method to nonlinear vibration problems can lead to a sequence of nonhomogeneous ordinary differential equations with periodic coefficients. The form of the complementary solutions are known from Floquet theory. This paper suggests a method for avoiding “secular terms” that grow with time in the particular solution.
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Generalization of the Floquet theory
Nonlinear Analysis: Theory, Methods & Applications, 2009Two systems of differential equations \(\omega\)-periodic in time are called topologically equivalent if there exists a mapping \(H(t,x)\) such that (i) \(H(t+\omega,x)=H(t,x)\); (ii) for any \(t\), \(H(t,. )\) is a homeomorphism; (iii) if \(x(t)\) is a solution of the first system, then \(H(t,x(t))\) is a solution of the second system.
Zou, Changwu, Shi, Jinlin
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Semiclassical many-mode floquet theory
Chemical Physics Letters, 1983Abstract It is shown that the single-mode Floquet formalism of Shirley can be extended to a generalized many-mode Floquet theory, yielding a practical non-perturbative technique for the semiclassical treatment of the interaction of a quantum system several monochromatic oscillating fields.
Tak-San Ho, Shih-I Chu, James V. Tietz
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Floquet Theory as a Computational Tool
SIAM Journal on Numerical Analysis, 2005Summary: We describe how classical Floquet theory may be utilized, in a continuation framework, to construct an efficient Fourier spectral algorithm for approximating periodic orbits. At each continuation step, only a single square matrix, whose size equals the dimension of the phase-space, needs to be factorized; the rest of the required numerical ...
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IEEE transactions on industrial electronics (1982. Print), 2021
Hong Li +5 more
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Hong Li +5 more
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Multiphoton Processes: Floquet Theory
2010The study of the interaction of intense laser fields with atoms and molecules has attracted considerable attention in recent years. In particular, the availability of increasingly intense lasers has made possible the observation of a wide variety of multiphoton processes, including multiphoton ionization, laser-assisted electron–atom collisions and ...
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Dynamic behavior analysis of tethered satellite system based on Floquet theory
Nonlinear dynamics, 2021G. Zhu +4 more
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Topological classification of Floquet metamaterials based on Floquet theory
2022Being driven by the goal of finding edge modes and of explaining the occurrence of edge modes in the case of time-modulated metamaterials in the high-contrast and subwavelength regime, we analyse the topological properties of Floquet-Lyapunov decompositions of periodically parameterized time-periodic ordinary differential equations.
Ammari, Habib, Kosche, Thea
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Smooth optimal control with Floquet theory
2012This paper describes an approach to construct temporally shaped control pulses that drive a quantum system towards desired properties. A parametrization in terms of periodic functions with pre-defined frequencies permits to realize a smooth, typically simple shape of the pulses; their optimization can be performed based on a variational analysis with ...
Bartels, Bj��rn, Mintert, Florian
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Floquet engineering of point-gapped topological superconductors
Physical review BNon-Hermitian systems exhibit two distinct topological classifications based on their gap structure: line-gap and point-gap topologies. Although point-gap topology is intrinsic to non-Hermitian systems, its systematic construction remains a challenge ...
Xiang Ji +3 more
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