Classical limit of the quantum Zeno effect by environmental decoherence
Classical limit of the quantum Zeno effect by environmental decoherence
复制标题
DOI：
10.1103/physreva.89.042116
复制
发表时间：
2014-04-24
影响因子：
2.9
通讯作者：
Halliwell, J. J.
中科院分区：
文献类型：
--
作者：
Bedingham, D.;Halliwell, J. J.
我们考虑一个点粒子在一维最初被限制在一个有限的空间区域，其状态是经常监测到该区域的投影算子。在无限频繁监控的极限下，国家永远不会逃离这个区域--这就是芝诺效应。与此相反，在相应的经典问题中，状态扩散到区域外，频繁监测只是简单地去除概率。本文的目的是显示如何芝诺效应消失在经典极限在这个和类似的例子。我们给出了一个一般性的参数表明，芝诺效应被抑制在存在的消相干机制，抑制历史之间的干扰。我们展示了这是如何明确地在两个例子中涉及到一个一维子空间的投影，并确定该过程的关键时间尺度。我们将这种理解扩展到我们感兴趣的主要问题，即空间区域中粒子的情况，通过将其耦合到散肩环境。光滑投影仪需要给问题适当的定义，这意味着存在一个动量截止和最小长度尺度。我们表明，从该地区的逃逸率接近经典预期的结果，因此芝诺效应被抑制，只要环境引起的波动的动量足够大。我们建立的时间尺度上的任意初始状态发展足够大的波动，以满足这一条件。我们将我们的结果与以前关于芝诺效应的（h）超过bar -> 0极限的工作联系起来。我们通过绘制密度矩阵的概率通量线来说明我们的结果（这相当于纯态情况下的玻姆轨迹）。这些都非常清楚地说明了芝诺和反芝诺效应，以及它们的抑制。我们的结果与我们早期的论文[Phys. Rev. A 88，022128（2013）]密切相关，证明了退相干对量子力学反射的抑制。
We consider a point particle in one dimension initially confined to a finite spatial region whose state is frequently monitored by projection operators onto that region. In the limit of infinitely frequent monitoring, the state never escapes from the region-this is the Zeno effect. In the corresponding classical problem, by contrast, the state diffuses out of the region with the frequent monitoring simply removing probability. The aim of this paper is to show how the Zeno effect disappears in the classical limit in this and similar examples. We give a general argument showing that the Zeno effect is suppressed in the presence of a decoherence mechanism which suppresses interference between histories. We show how this works explicitly in two examples involving projections onto a one-dimensional subspace and identify the key time scales for the process. We extend this understanding to our main problem of interest, the case of a particle in a spatial region, by coupling it to a decohering environment. Smoothed projectors are required to give the problem proper definition and this implies the existence of a momentum cutoff and minimum length scale. We show that the escape rate from the region approaches the classically expected result, and hence the Zeno effect is suppressed, as long as the environmentally induced fluctuations in momentum are sufficiently large. We establish the time scale on which an arbitrary initial state develops sufficiently large fluctuations to satisfy this condition. We link our results to earlier work on the (h) over bar -> 0 limit of the Zeno effect. We illustrate our results by plotting the probability flux lines for the density matrix (which are equivalent to Bohm trajectories in the pure-state case). These illustrate both the Zeno and anti-Zeno effects very clearly, and their suppression. Our results are closely related to our earlier paper [Phys. Rev. A 88, 022128 (2013)], demonstrating the suppression of quantum-mechanical reflection by decoherence.