Stable and unstable diagram of the Mathieu equation. Each ai (i = 0, 1, 2, …) is an eigenvalue of even periodic solutions cei of the Mathieu equation (dashed line). Any curve of eigenvalue bj (j = 1, 2, …) corresponds to the odd periodical solution sej (solid line). The stable and unstable solution of the Mathieu equation corresponds to the blank areas and shaded areas, respectively."
Figure 1.
Figure 2.
The stable dynamics for λ = 2, q = 0.1. The peaks of momentum distribution and dynamical structure factor synchronously emerge except $\tau =(2n+1)\pi /4,n\,=\,0,1,2,\ldots $, which shows a strong relation of one-body property and two-body correlation."
Figure 2.
Figure 3.
The unstable dynamics for λ = 1, q = 0.1. The evolving dynamical structure factor and momentum distribution are all exponentially increasing. The evolving dynamical structure factor has evident peak structure, while the momentum distribution becomes flat at $\tau =(2n+1)\pi /4$."
McLachlan N W 1951 Theory and Application of Mathieu Functions Oxford Oxford University Press
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Abramowitz M Stegun I A 1948 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables Washington, DC US Government Printing Office
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Wang Z X Guo D R 1989 Special Functions Singapore World Scientific
),Z C Tu(涂展春)
