超指数自作用振荡器
Superexponential Self-Interacting Oscillator
摘要：
介绍并分析了超指数自作用振荡器（SSO）。它的幂律势的特征在于基和指数都依赖于振子的动力学变量。相对于标准的振荡器，如（一）谐波振荡器，SSO结合了散射和约束的周期性运动与指数变化的非线性。SSO势存在一个过渡点，该过渡点具有对数和幂律奇异性的层次结构，在其相空间曲线的聚集中留下了它们的指纹。因此，当经过跃迁能量时，SSO的周期经历了从线性下降到非线性增加行为的交叉。我们探讨其动态，并表明，交叉涉及踢样行为。一个对称的双阱变种的SSO进行了简要讨论。
英文摘要：
The superexponential self-interacting oscillator (SSO) is introduced and analyzed. Its power law potential is characterized by the dependence of both the base and the exponent on the dynamical variable of the oscillator. Opposite to standard oscillators such as the (an-)harmonic oscillator the SSO combines both scattering and confined periodic motion with an exponentially varying nonlinearity. The SSO potential exhibits a transition point with a hierarchy of singularities of logarithmic and power law character leaving their fingerprints in the agglomeration of its phase space curves. The period of the SSO consequently undergoes a crossover from decreasing linear to a nonlinearly increasing behaviour when passing the transition energy. We explore its dynamics and show that the crossover involves a kick-like behaviour. A symmetric double well variant of the SSO is briefly discussed.
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