双频激励与应变超晶格的倍频共振

Dual-frequency Excitation and Multiplier Frequency Resonance of Strained Superlattice

摘要:

假设超晶格锯齿形沟道对粒子的作用等效为形状相似的周期场作用，在经典力学框架内和小振幅近似下，利用正弦平方势，把粒子运动方程化为了具有双频激励的Duffing方程。由于三阶非线性，系统出现了主共振、次共振和组合共振等。用摄动法分析了系统的倍频共振，并讨论了系统的稳定性和临界条件。结果表明，当非线性强度小于临界强度时系统是稳定的。

Abstract:

It is assumed that the effect of superlattice sawtooth shaped channel on particles is equivalent to the periodic field of a similar shape. Under the framework of classical mechanics and small amplitude approximation, the motion equation of particles is reduced to Duffing equation with a dual frequency excitation by using the sine squared potential. Due to the third order nonlinearity, there are main resonance, sub resonance, combination resonance，etc in the system. Multi frequency resonance was analyzed by perturbation method, and the stability and the critical conditions of the system were discussed. The results show that the system is stable when the nonlinear strength is less than the critical intensity.