论文标题
连续投影测量下的量子动力学：非热式描述和连续空间极限
Quantum Dynamics under continuous projective measurements: non-Hermitian description and the continuous space limit
论文作者
论文摘要
在重复测量协议的框架中考虑了量子系统以指定状态的到达时间的问题，特别是讨论了连续测量的限制。结果表明，对于特定的系统检测器耦合，可以避免ZENO效应，并且可以通过非炎性有效的哈密顿量有效地描述系统。作为一个特定示例，我们考虑量子粒子在一维晶格上的演变，该晶格受到特定位点的位置测量。通过求解相应的非热波函数进化方程，我们提出了有关生存概率和首次到达时间分布的分析闭合形式的结果。最后，我们讨论了消失的晶格间距的极限，并表明这导致了连续描述，其中粒子通过探测器位点的复杂的robin边界条件通过游离的schrodinger方程而演变。提出了这种动态的几个有趣的物理结果。
The problem of the time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol and in particular the limit of continuous measurements is discussed. It is shown that for a particular choice of system-detector coupling, the Zeno effect is avoided and the system can be described effectively by a non-Hermitian effective Hamiltonian. As a specific example we consider the evolution of a quantum particle on a one-dimensional lattice that is subjected to position measurements at a specific site. By solving the corresponding non-Hermitian wave function evolution equation, we present analytic closed-form results on the survival probability and the first arrival time distribution. Finally we discuss the limit of vanishing lattice spacing and show that this leads to a continuum description where the particle evolves via the free Schrodinger equation with complex Robin boundary conditions at the detector site. Several interesting physical results for this dynamics are presented.
