论文标题
Feynman Checkers：迈向算法量子理论
Feynman checkers: towards algorithmic quantum theory
论文作者
论文摘要
我们调查和开发由R $。$ Feynman引入的最基本的电子运动模型。在此游戏中，Checker通过简单的规则在棋盘上移动，我们计算转弯。 Feynman Checkers也被称为一维量子步行或在假想温度下的ISING模型。我们从数学上解决了一个问题。$ $。$ FEYNMAN，从1965年开始，这是为了证明离散模型（在很大的时间内，平均速度和小晶格步骤）与连续体一致。我们研究了该模型的渐近性能（对于小晶格步骤和大时间），从1972年开始将结果提高到J $。$ NARLIKAR，并以t $。$。$ SUNADA-T $。$。$ tate。从2012年起，我们首次观察并证明了小型局部速度限制中的度量浓度。我们执行模型的第二个量化。
We survey and develop the most elementary model of electron motion introduced by R$.$Feynman. In this game, a checker moves on a checkerboard by simple rules, and we count the turns. Feynman checkers are also known as a one-dimensional quantum walk or an Ising model at imaginary temperature. We solve mathematically a problem by R$.$Feynman from 1965, which was to prove that the discrete model (for large time, small average velocity, and small lattice step) is consistent with the continuum one. We study asymptotic properties of the model (for small lattice step and large time) improving the results by J$.$Narlikar from 1972 and by T$.$Sunada-T$.$Tate from 2012. For the first time we observe and prove concentration of measure in the small-lattice-step limit. We perform the second quantization of the model.
