First, we focused on understanding the role of quantum coherence in simple transport devices. We used techniques from quantum walks and quantum transport to understand toy models of particle transport, and the role of coherences in them. We then added quantum decoherence, also know as dephasing. This dephasing can come, for example, from electron-phonon couplings. We studied its role in different geometries, to show how dephasing and quantum interference can be used to control transport in some devices in general. This provides a new quantum way to contro heat and electronic flow and was published in one paper. We then used more powerful ab-initio techniques for more realistic and interesting thermo-electric molecular devices. We demonstrated that the current and heat flows are not only dictated by the temperature and potential gradient, but also by the external action of a local quantum observer that controls the coherence of the device. Depending on how and where the observation took place, the direction of heat and particle currents were independently controlled. In fact, we showed that the current and heat flow in a quantum material can go against the natural temperature and voltage gradients. Dynamical quantum observation offers new possibilities for the control of quantum transport far beyond classical thermal reservoirs. Through the concept of local projections, we illustrate how we can create and directionality control the injection of currents (electronic and heat) in nanodevices. This scheme provides novel strategies to construct quantum devices with application in thermoelectrics, spintronic injection, phononics, and sensing among others. This was published as another major publications
Second, we developed new techniques to fundamentally characterize and understand unknown quantum processes, such as those coming from molecular devices. There was no systematic way to describe a quantum process with memory solely in terms of experimentally accessible quantities. We develope a universal framework to characterize arbitrary non-Markovian quantum processes. We show how a multitime non-Markovian process can be reconstructed experimentally, and that it has a natural representation as a many-body quantum state, where temporal correlations are mapped to spatial ones. Moreover, this state is expected to have an efficient matrix-product-operator form in many cases. Our framework constitutes a systematic tool for the effective description of memory-bearing open-system evolutions in quantum transport devices. We also derived a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by accounting for all potentially detectable memory effects. We then derive a family of measures of non-Markovianity with clear operational interpretations which is crucial for understanding the underlying dynamics and fluctuations.
Lastly, we then used these things known to start to develop some new TD-DFT functionals. We have tested some final temperature open system functionals, are currently iterating them to improve them for publication.
