Exact description of quantum stochastic models as quantum resistors

Diffusion is one of the most common transport phenomena at hydrodynamic scales, both in classical and quantum systems. Yet, how exactly diffusion emerges from the underlying microscopic theory in a quantum system is still an exciting open question.

In this talk, we present a new method to derive the transport properties of diffusive/ohmic quantum systems connected to fermionic reservoirs. The method is based on the expansion of the current in terms of the inverse system size using Keldysh formalism. We apply it to a large class of exactly solvable quantum stochastic Hamiltonians (QSHs) with time and space-dependent noise. These models confirm the validity of our system size expansion ansatz and its efficiency in capturing the transport properties. In particular, we consider three fermionic models: i) a model with local dephasing ii) the quantum simple symmetric exclusion process model iii) a model with long-range stochastic hopping. As a by-product, our approach equally describes the mean behavior of quantum systems under continuous measurement.