The ghost-box-ball system: A unified perspective on soliton cellular automata, the RSK algorithm and phase shifts

Nicholas M. Ercolani, Jonathan Ramalheira-Tsu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper, we introduce the ghost-box-ball system, which is an extended version of the classical soliton cellular automaton. It is initially motivated as a mechanism for making precise a connection between the Schensted insertion (of the Robinson–Schensted–Knuth correspondence) and the dynamical process of the box-ball system. In addition to this motivation, we explore generalisations of classical notions of the box-ball system, including the solitonic phenomenon, the asymptotic sorting property, and the invariant shape construction. We analyse the ghost-box-ball system beyond its initial relevance to the Robinson–Schensted–Knuth correspondence, unpacking its relationship to its underlying dynamical evolution on a coordinatisation and using a mechanism for augmenting a regular box-ball configuration to study the classical ultradiscrete phase shift phenomenon.

Original languageEnglish (US)
Article number132986
JournalPhysica D: Nonlinear Phenomena
Volume426
DOIs
StatePublished - Nov 15 2021

Keywords

  • Box-ball system
  • Cellular automata
  • Phase shift
  • RSK correspondence
  • Soliton
  • Ultradiscretization

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'The ghost-box-ball system: A unified perspective on soliton cellular automata, the RSK algorithm and phase shifts'. Together they form a unique fingerprint.

Cite this