Analytical results for a coagulation/decoagulation model on an inhomogeneous lattice

TL;DR

This paper maps an inhomogeneous coagulation/decoagulation lattice model to a quadratic fermionic system, computes its spectrum exactly, and analyzes the spectral gap, extending previous homogeneous models with impurity-based inhomogeneity.

Contribution

It introduces an exact spectral analysis of an inhomogeneous coagulation/decoagulation model using Jordan-Wigner transformation, incorporating impurity effects.

Findings

Exact spectrum computed for inhomogeneous model

Spectral gap characterized for specific examples

Model constructed from two homogeneous models with a special bond

Abstract

We show that an inhomogeneous coagulation/decoagulation model can be mapped to a quadratic fermionic model via a Jordan-Wigner transformation. The spectrum for this inhomogeneous model is computed exactly and the spectral gap is described for some examples. We construct our inhomogeneous model from two different homogeneous models joined by one special bond (impurity). The homogeneous models we started with are the coagulation/decoagulation models studied previously using the Jordan-Wigner transformation.