Construction and Analysis of the Effective Model for the Bulk Steady State under Current in Boundary-Driven Open Systems

TL;DR

This paper introduces an effective asymmetric-hopping model to analyze steady states in boundary-driven open systems, revealing a linear increase in effective temperature with current density, aiding in distinguishing intrinsic effects from Joule heating.

Contribution

The paper develops a translationally invariant effective bulk model for boundary-driven systems, including a minimal case related to the Hatano--Nelson model, to analyze current-induced phenomena.

Findings

Effective temperature rises linearly with current density.

Model helps separate intrinsic effects from Joule heating.

Corresponds to an open-system Hatano--Nelson model in minimal case.

Abstract

Current-induced phenomena are often obscured by Joule heating, and their steady states are difficult to analyze in large open systems. We introduce a translationally invariant asymmetric-hopping model as an effective bulk description of boundary-driven systems under current. In a minimal case, it corresponds to an open-system Hatano--Nelson model. We find that the effective temperature rises linearly with current density, as observed experimentally. The model provides a useful tool for separating intrinsic current-induced effects from heating.