Additivity Principle in High-dimensional Deterministic Systems

TL;DR

This paper investigates the additivity principle in three-dimensional disordered harmonic lattices, demonstrating its validity across different transport regimes and emphasizing the role of dimensionality in heat transfer behavior.

Contribution

It extends the additivity principle to high-dimensional deterministic systems and analyzes its applicability in ballistic, diffusive, and anomalous transport regimes.

Findings

Additivity principle holds in diffusive regime for 3D systems.

CGF matches AP predictions even in anomalous transport.

Dimensionality influences the validity of the additivity principle.

Abstract

The additivity principle (AP), conjectured by Bodineau and Derrida [Phys. Rev. Lett. vol.92, 180601 (2004)], is discussed for the case of heat conduction in three-dimensional disordered harmonic lattices to consider the effects of deterministic dynamics, higher dimensionality, and different transport regimes, i.e., ballistic, diffusive, and anomalous transport. The cumulant generating function (CGF) for heat transfer is accurately calculated, and compared with the one given by the AP. In the diffusive regime, we find a clear agreement with the conjecture even if the system is high-dimensional. Surprisingly even in the anomalous regime the CGF is also well fitted by the AP. Lower dimensional systems are also studied and the importance of three-dimensionality for the validity is stressed.