Thermodynamics and Transport in Mesoscopic Disordered Networks

TL;DR

This paper investigates how phase coherence influences transport and thermodynamic properties in mesoscopic disordered networks, linking magnetic response to diffusion processes and spectral functions across various network geometries.

Contribution

It introduces a method to calculate magnetic response in mesoscopic networks using diffusion equations and spectral functions, extending understanding of phase coherence effects.

Findings

Magnetization of connected rings is comparable to disconnected rings.

Magnetic response relates to the return probability of diffusive particles.

Spectral function captures the essence of phase coherence effects.

Abstract

We describe the effects of phase coherence on transport and thermodynamic properties of a disordered conducting network. In analogy with weak-localization correction, we calculate the phase coherence contribution to the magnetic response of mesoscopic metallic isolated networks. It is related to the return probability for a diffusive particle on the corresponding network. By solving the diffusion equation on various types of networks, including a ring with arms, an infinite square network or a chain of connected rings, we deduce the magnetic response. As it is the case for transport properties --weak-localization corrections or universal conductance fluctuations-- the magnetic response can be written in term of a single function S called spectral function which is related to the spatial average of the return probability on the network. We have found that the magnetization of an ensemble of CONNECTED rings is of the same order of magnitude as if the rings were disconnected.