Equivalent Resistance from the Quantum to the Classical Transport Limit.

We generalize the concept of equivalent resistance to the entire range from coherent quantum to diffusive classical transport by introducing the notion of transport equivalent networks. We show that this novel concept presents us with a platform to simplify the structure of quantum networks while preserving their global and local transport properties, even in the presence of electron-phonon or electron-electron interactions. This allows us to describe the evolution of equivalent quantum networks to equivalent classical resistor networks with increasing interaction strength.