论文标题
在晶格上过渡到量子力学的经典制度和不连续空间的含义
Transition to the classical regime in quantum mechanics on a lattice and implications of discontinuous space
论文作者
论文摘要
众所周知，由于不确定性原理，普朗克常数在相空间中设定了一个分辨率边界，并且已经彻底研究了不兼容测量之间的分辨率折衷。还知道，在经典制度中，可以同时确定位置和动量的足够粗糙的测量。但是，当我们从量子过渡到经典制度时，不确定性原理如何逐渐消失的情况并不那么生动。在目前的工作中，我们通过研究量化不确定性原理在有限维量子力学对晶格的框架中的影响的相关概率来阐明这张照片。我们还研究了这些概率如何受到晶格的粒度的扰动，并表明它们可以向基础空间的不连续性发出信号。
It is well known that, due to the uncertainty principle, the Planck constant sets a resolution boundary in phase space and the resulting trade-off in resolution between incompatible measurements has been thoroughly investigated. It is also known that, in the classical regime, sufficiently coarse measurements of position and momentum can simultaneously be determined. However, the picture of how the uncertainty principle gradually disappears as we transition from the quantum to the classical regime is not so vivid. In the present work we clarify this picture by studying the associated probabilities that quantify the effects of the uncertainty principle in the framework of finite-dimensional quantum mechanics on a lattice. We also study how these probabilities are perturbed by the granularity of the lattice and show that they can signal the discontinuity of the underlying space.
