重复弱测量中动态不连续性通过复弱值揭示
Dynamical discontinuities in repeated weak measurements revealed by complex weak values
AI总结：
研究通过复弱值揭示重复弱测量与后选择可产生非解析动态响应，改变量子动态稳定性结构。
摘要：
本文证明了重复弱测量与后选择可以产生米观测量中的尖锐动态不连续性，即使是在最小的量子系统中。这种不连续行为由后选择状态的极角控制，这是一个连续的控制参数。当这个角度变化时，米观测量的期望值在关联弱值的虚部变为零的点处突然变化。这种非解析行为仅在弱值在一定范围内真正复数时才会出现。如果弱值对所有角度都保持纯实数，则动态保持平滑。不连续性源于非幺正Kraus算符固定点之间稳定性交换。值得注意的是，尽管没有热力学极限，不连续性附近弛豫时间表现出普遍的临界行为，其临界指数等于1，与系统参数无关。这些结果确立了弱值作为可调控制参数的能力，能够诱导非解析的动态响应并重塑测量诱导的量子动态的稳定性结构。
英文摘要：
This work demonstrates that repeated weak measurements together with post-selection can produce sharp dynamical discontinuities in meter observables, even in minimal quantum systems. The discontinuous behavior is governed by the polar angle of the post selected state, which serves as a continuous control parameter. As this angle is varied, the expectation value of the meter observables changes abruptly at the point where the imaginary part of the associated weak value, a complex quantity that arises in weak measurements with post-selection, becomes zero. Such non-analytic behavior emerges only when the weak value is genuinely complex for a range of post-selection angles. If the weak value remains purely real for all angles, the dynamics remain smooth. The discontinuity originates from an exchange of stability between fixed points of the non-unitary Kraus operator governing the meter's evolution. Remarkably, despite the absence of a thermodynamic limit, the relaxation time in the vicinity of the discontinuity exhibit universal critical behavior characterized by a critical exponent equal to $1$, independent of system parameters. These results establish the weak value as a tunable control parameter capable of inducing non-analytic dynamical responses and reshaping the stability structure of measurement-induced quantum dynamics.
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