Exactly solvable reaction diffusion models on a Cayley tree

TL;DR

This paper introduces and solves exactly a general reaction-diffusion model on a Cayley tree, analyzing its stationary states and dynamics, including the spectrum of the evolution Hamiltonian which indicates finite relaxation times.

Contribution

It presents the first exact solution for a broad class of reaction-diffusion models on Cayley trees using the empty-interval method.

Findings

The model's spectrum is discrete, indicating finite relaxation times.

Stationary solutions and dynamics are explicitly characterized.

The model is exactly solvable for nearest-neighbor interactions.

Abstract

The most general reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics, are discussed. Concerning the dynamics, the spectrum of the evolution Hamiltonian is found and shown to be discrete, hence there is a finite relaxation time in the evolution of the system towards its stationary state.