A quantization of interacting particle systems
Quantum Physics
2024-03-26 v2 Mathematical Physics
math.MP
Number Theory
Probability
Abstract
Interacting particle systems studied in this paper are probabilistic cellular automata with nearest-neighbor interaction including the Domany-Kinzel model. A special case of the Domany-Kinzel model is directed percolation. We regard the interacting particle system as a Markov chain on a graph. Then we present a new quantization of the interacting particle system. After that, we introduce a zeta function of the quantized model and give its determinant expression. Moreover, we calculate the absolute zeta function of the quantized model for the Domany-Kinzel model.
Cite
@article{arxiv.2402.00280,
title = {A quantization of interacting particle systems},
author = {Jirô Akahori and Norio Konno and Rikuki Okamoto and Iwao Sato},
journal= {arXiv preprint arXiv:2402.00280},
year = {2024}
}
Comments
16 pages