IPS/Zeta Correspondence

TL;DR

This paper introduces a new zeta function for multi-particle interacting systems, extending previous work on single-particle models, and computes it for specific tensor-type models.

Contribution

It presents a novel zeta function for multi-particle IPSs with interactions, expanding the mathematical framework for analyzing complex stochastic and quantum systems.

Findings

Derived the zeta function for certain tensor-type IPSs

Extended the Konno-Sato theorem to multi-particle models

Provided computational methods for the new zeta function

Abstract

Our previous works presented zeta functions by the Konno-Sato theorem or the Fourier analysis for one-particle models including random walks, correlated random walks, quantum walks, and open quantum random walks. This paper introduces a new zeta function for multi-particle models with probabilistic or quantum interactions, called the interacting particle system (IPS). We compute the zeta function for some tensor-type IPSs.