We can see and feel (and even hear and smell) what current flow can do in lightbulbs. So how about the thinnest wires possible in nature: chains of single atoms, which can be made with high control?
The difference is not just size. The current densities (current/cross-section) in lightbulbs are say 108 A/m2. In atomic wires they reach 1015 A/m2. What happens to the electrons and the nuclei under these conditions is an open question, to both experiment and theory.
A lot has been achieved and learned about these conducting systems, and a range of methodologies exists depending on the questions to address. Our interest is in describing how these extraordinary currents interact with the atomic motion, and what happens to the latter as a consequence of this. Atomic chains can heat up much more than was initially imagined, with atoms reaching local temperatures than could even melt the metal.
Even more exotic phenomena have been identified and are being studied.
This project, in collaboration with colleagues here, in the Netherlands and Denmark, will develop and exploit a dynamical statistical mechanics method that generates an equation of the Fokker-Planck type to describe atomic motion in quantum wires. It is not a classical equation though, and subsumes both the electron-phonon interaction and quantum aspects of the motion of the atoms.
The project would require a balanced interest in pen-and-paper work, in calculations and experiment. Transport theory and quantum mechanics for non-equilibrium interacting open systems are the main areas involved.
T. N. Todorov, D. Dundas, J-T Lu, M. Brandbyge and P. Hedegard: Current induced forces: a simple derivation (2014) Eur. J. Phys. 35 065004