时间周期驱动的非线性无序系统的传输阈值
Transmission thresholds in time-periodically driven nonlinear disordered systems
摘要：
研究了局域时间周期驱动的无序非线性链中能量的传播。对于线性安德森模式带内的频率，随着驱动振幅的增加，观察到三种不同的区域：1）低于阈值，局部准周期振荡和无扩展; 2）接近阈值的时间上的三种不同区域，初始几乎规则振荡，中间时间的弱混沌和缓慢扩展，最后是强扩散; 3）强驱动的立即扩展。阈值是由于简单的分叉，获得解析为一个单一的振荡器，和数值上的非线性响应流形的转折点为一个完整的链。一般来说，对于无限链，阈值也是非零的。
英文摘要：
We study energy propagation in locally time-periodically driven disordered nonlinear chains. For frequencies inside the band of linear Anderson modes, three different regimes are observed with increasing driver amplitude: 1) Below threshold, localized quasiperiodic oscillations and no spreading; 2) Three different regimes in time close to threshold, with almost regular oscillations initially, weak chaos and slow spreading for intermediate times, and finally strong diffusion; 3) Immediate spreading for strong driving. The thresholds are due to simple bifurcations, obtained analytically for a single oscillator, and numerically as turning-points of the nonlinear response manifold for a full chain. Generically, the threshold is nonzero also for infinite chains.
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