Current Fluctuations in One-Dimensional Diffusion-Reaction Systems via Tensor Networks

TL;DR

This paper uses tensor network methods to analyze current fluctuations in one-dimensional diffusion-reaction systems, revealing how reactions influence fluctuation bounds and confirming the fluctuation theorem.

Contribution

It introduces a tensor network approach to compute the full counting statistics of current in diffusion-reaction systems, demonstrating the damping effect of reactions on fluctuations.

Findings

Reactions dampen current fluctuations.

The fluctuation theorem holds for the system.

Current fluctuations are upper bounded by reactions.

Abstract

Tensor networks are employed to characterize the current fluctuations in one-dimensional diffusion-reaction systems. The representative system under study is a semiconducting material where holes and electrons constitute two types of charge carriers. These holes and electrons diffuse in the system with the reactions of pair-generation and -recombination occurring between them. The system is driven by imbalanced conditions imposed at two boundaries. The large deviation function encoding the full counting statistics of electric current is numerically calculated using the density matrix renormalization group. The fluctuation theorem is shown to hold for the current. Moreover, by comparing the cases where the reactions are turned on or off, it is revealed that the reactions have a damping effect on current fluctuations. This indicates an interesting inequality, suggesting that current fluctuations are upper bounded.