势阱中的混沌及其量子对应

Chaos in Potential Well and Classical-Quantum Correspondence

通过数值计算,研究了势阱谐振子耦合系统的经典动力学,发现随着能量E越低,或势阱阱宽2A越宽,或耦合系数λ越大,系统混沌程度越强.通过不同条件下最近邻能级间距分布与对应的经典动力学比较发现量子-经典结果符合得很好.对一些低能疤痕量子态找到了与其对应的经典周期轨道.

This paper numerically studied the classical dynamics for the coupled potential well and the Harmonic oscillator system. It is found that the lower the system energy,or the wider the width of the potential well,or the larger the coupling constant,the stronger the chaos. By comparing with the nearest neighbor spacing distribution of energy levels,we found that the quantum results agree with the classical results very well. For some low energy quantum scaring states,we found the corresponding classical periodic orbits.