Box and Ball System with Numbered Boxes

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2022-04-24 DOI:10.1007/s11040-022-09425-6

Yusaku Yamamoto, Akiko Fukuda, Sonomi Kakizaki, Emiko Ishiwata, Masashi Iwasaki, Yoshimasa Nakamura

引用次数: 0

Abstract

The box and ball system (BBS) models the dynamics of balls moving among an array of boxes. The simplest BBS is derived from the ultradiscretization of the discrete Toda equation, which is one of the most famous discrete integrable systems. The discrete Toda equation can be extended to two types of discrete hungry Toda (dhToda) equations, one of which is the equation of motion of the BBS with numbered balls (nBBS). In this paper, based on the ultradiscretization of the other type of dhToda equation, we present a new nBBS in which not balls, but boxes, are numbered. We also investigate conserved quantities with respect to balls and boxes, the solitonical nature of ball motions, and a scattering rule in collisions of balls to clarify the characteristics of the resulting nBBS.

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带编号盒子的盒子和球系统

盒子和球系统(BBS)模拟球在一组盒子之间运动的动力学。最简单的BBS是由离散Toda方程的超离散化导出的，Toda方程是最著名的离散可积系统之一。离散Toda方程可推广为两类离散饥饿Toda方程(dhToda)，其中一类是带编号球的BBS运动方程(nBBS)。本文在对另一类dhToda方程进行超离散化的基础上，提出了一种新的非球而盒的nBBS。我们还研究了关于球和盒子的守恒量，球运动的孤子性质，以及球碰撞中的散射规则，以阐明由此产生的nBBS的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.