We present a formal extension of the Pauli exclusion principle to the arbitrary-order jumping up and down excited Schrödinger’s cats. We show that the excited symmetric Schrödinger’s cat of the n-order will occupy the same n-order excited eigenstate of the harmonic oscillator when the “alive” and “dead” cat’s constituents closely approach in space and time each other. The antisymmetric n-order cat states, vice versa, will never occupy the same excited n-order eigenstate. For example, the respective probabilities for antisymmetric cat states of n = 1, 2, and 3 orders to jump up onto the corresponding energy levels with n = 2, 3,and 4, and, at the same time, jump down onto the levels with n = 0, 1, and 2, are found to be in the ratios: 2/3:1/3, 3/5:2/5, and 4/7:3/7, with the asymptotic saturated ratio of 1/2:1/2 for the cat states distributed over the higher-energy levels. Moreover, we demonstrate the remarkable analogies between linear and nonlinear dynamics of the higher-order Schrödinger’s cats revealed in the framework of the nonlinear Schrödinger equation model with harmonic oscillator potential.

我们将保利排斥原理的形式扩展扩展为兴奋薛定ding猫的任意阶跃。我们表明，当“活”和“死”猫的成分在空间和时间上彼此接近时，n阶对称的对称对称薛定ding猫将占据谐波振荡器的相同n阶激发本征态。反对称的n阶猫状态反之亦然，将永远不会占据相同的激发n阶本征态。例如，n = 1、2和3个阶的非对称猫状态的相应概率跳到n = 2、3和4的相应能级，同时又跳到相应的能级n = 0、1和2的比率为：2/3：1 / 3、3 / 5：2/5和4/7：3/7，渐近饱和比率为1 / 2：猫状态的1/2分布在较高能级上。此外，我们证明了在具有谐振子势能的非线性Schrödinger方程模型框架中揭示的高阶Schrödinger猫的线性和非线性动力学之间的非凡类比。