AI 中文总结
研究带节点的量子波函数自由演化最优性，基于与二次最优传输成本相关泛函，发现有节点时为局部最小，无节点时为全局最小，揭示自由量子演化中节点存在内在不稳定性。
AI 中文摘要
扩展和完善先前工作，考虑量子波函数在允许节点存在的一般情形下具有固定初始和最终模的自由演化。方法基于考虑与离散时间二次最优传输成本相关的合适简单泛函。在合理假设下表明，若存在节点，具有固定初始和最终模的波函数自由演化是一种局部最小值；若不存在节点则最小值是全局的，这表明自由量子演化中节点存在内在不稳定性。
英文摘要
Extending and refining a preceding work, the free evolution of a quantum wave function, with fixed initial and final modulus, is considered in the general case where nodes are allowed. The method is based on considering a suitable simple functional related to the quadratic optimal transport cost in discrete time. Under reasonable assumptions it is shown that, if nodes are present, the free evolution of the wave function with fixed initial and final modulus is a sort of local minimum. If no nodes are present the minimum is global, suggesting intrinsic instability of the nodes in a free quantum evolution.
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