论文标题
Feynman Checkers：方向逆转的可能性
Feynman checkers: the probability of direction reversal
论文作者
论文摘要
我们研究了R.Feynman于1965年引入的最基本的电子运动模型。这是一款游戏，在该游戏中，Checker通过简单的规则在棋盘上移动，我们计算转弯。该模型也称为一维量子步行。 R.Feynman在他的出版物中引入了路径积分的离散版本，并在晶格步骤和平均速度倾向于零并且时间趋于无限时提出了计算模型限制的问题。在简单的特殊情况下，我们在严格的数学层面上的问题上取得了非平凡的进步。即使是这种情况也需要以前未知的方法。我们还证明了I.Gaidai-Turlov，T.Kovalev和A.lvov的猜想，其方向逆转的极限可能性在模型中推广了A.ustinov的最新结果。
We study the most elementary model of electron motion introduced by R.Feynman in 1965. It is a game, in which a checker moves on a checkerboard by simple rules, and we count the turnings. The model is also known as one-dimensional quantum walk. In his publication, R.Feynman introduces a discrete version of path integral and poses the problem of computing the limit of the model when the lattice step and the average velocity tend to zero and time tends to infinity. We get a nontrivial advance in the problem on the mathematical level of rigor in a simple particular case; even this case requires methods not known before. We also prove a conjecture by I.Gaidai-Turlov, T.Kovalev, and A.Lvov on the limit probability of direction reversal in the model generalizing a recent result by A.Ustinov.
