Thermodynamics and transport in mesoscopic disordered networks

Abstract

We describe the effects of phase coherence on transport and thermodynamic properties of a disordered conducting network. In analogy with the weak-localization correction. we calculate the phase coherent 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 is the case for transport properties (weak-localization corrections or universal conductance fluctuctions) the magnetic response can be written in terms of a single function S called the 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.