费曼跳棋:数论性质

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Reviews in Mathematical Physics Pub Date : 2022-10-13 DOI:10.1142/s0129055x23500228

Fedor Kuyanov, Alexey Slizkov

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引用次数: 2

摘要

我们研究了由R.Feynman提出的电子运动的基本模型Feynman跳棋。在这个模型中，一个方格在棋盘上移动，我们计算转弯次数。费曼跳棋也被称为一维量子行走。我们在这个模型中证明了一些新的数论结果，例如，电子波函数的实部和虚部在特定区域的符号交替。我们所有的结果都可以用杨图来表示，也就是说，我们将杨图的数量与奇数和偶数步数进行比较。

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Feynman checkers: number-theoretic properties

We study Feynman checkers, an elementary model of electron motion introduced by R. Feynman. In this model, a checker moves on a checkerboard, and we count the turns. Feynman checkers are also known as a one-dimensional quantum walk. We prove some new number-theoretic results in this model, for example, sign alternation of the real and imaginary parts of the electron wave function in a specific area. All our results can be stated in terms of Young diagrams, namely, we compare the number of Young diagrams with an odd and an even number of steps.

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来源期刊

Reviews in Mathematical Physics 物理-物理：数学物理

CiteScore

3.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Reviews in Mathematical Physics fills the need for a review journal in the field, but also accepts original research papers of high quality. The review papers - introductory and survey papers - are of relevance not only to mathematical physicists, but also to mathematicians and theoretical physicists interested in interdisciplinary topics. Original research papers are not subject to page limitations provided they are of importance to this readership. It is desirable that such papers have an expository part understandable to a wider readership than experts. Papers with the character of a scientific letter are usually not suitable for RMP.