Reduction of periodic one-dimensional hopping model

TL;DR

This paper discusses methods to simplify complex periodic one-dimensional hopping models into one- or two-state models while preserving essential properties, enabling easier analysis of similar processes.

Contribution

It introduces reduction techniques that allow complex hopping models to be approximated by simpler models without losing key characteristics.

Findings

Reduction methods effectively approximate complex models

Simple models retain essential properties of original processes

Many processes can be described by one- or two-state models

Abstract

In this research, methods of reducing a general periodic one-dimensional hopping model to a one- or two-state model, which keeps the basic properties of the original process, are discussed. This reduction also implies that, to some extent, many processes can be well described by simple two-state or even one-state models.