点相互作用量子系统中波包的不可逆行为与坍缩
Irreversible Behaviour and Collapse of Wave Packets in a Quantum System with Point Interactions
摘要：
一个粒子与一个谐振子的系统，如果不耦合，则具有纯点谱，当粒子与谐振子通过足够强的点相互作用耦合时，已知获得绝对连续谱。这里揭示了这种现象背后的简单动力学机制。振荡器的能量被证明是指数发散的时间，而粒子的空间概率分布崩溃到一个三角函数的相互作用点。基于这一结果，本文提出了一个广义模型，该模型包含多个在不同点与粒子相互作用的振子，从而为位置的近似测量和波包的坍缩提供了一个形式化的模型。
英文摘要：
A system of a particle and a harmonic oscillator, which have pure point spectrum if uncoupled, is known to acquire absolutely continuous spectrum when the particle and the oscillator are coupled by a sufficiently strong point interaction. Here the simple dynamical mechanism underlying this phenomenon is exposed. The energy of the oscillator is proven to exponentially diverge in time, while the spatial probability distribution of the particle collapses into a delta function in the interaction point. On account of this result, a generalized model with many oscillators which interact with the particle at different points is argued to provide a formal model for approximate measurement of position, and collapse of wave packets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
