The eigenpairs of a Sylvester-Kac type matrix associated with a simple model for one-dimensional deposition and evaporation

TL;DR

This paper derives eigenvalues and eigenvectors for a Sylvester-Kac type matrix arising from a simple model of deposition and evaporation on finite discrete arrays, applicable to various related models.

Contribution

It provides a general solution for eigenpairs of Sylvester-Kac type matrices for any number of cells, extending previous specific cases.

Findings

Eigenvalues and eigenvectors explicitly determined for the matrix

Applicable to a wide range of deposition-evaporation models

Provides a basis for analyzing dynamics of such systems

Abstract

A straightforward model for deposition and evaporation on discrete cells of a finite array of any dimension leads to a matrix equation involving a Sylvester-Kac type matrix. The eigenvalues and eigenvectors of the general matrix are determined for an arbitrary number of cells. A variety of models to which this solution may be applied are discussed.