Orbital Wigner functions and quantum transport in multiband systems

Traditional semiclassical transport theories in metals are based on the Boltzmann equation and discard quantum coherent effects. However, recent experiments, such as ultracold atom realizations of multiband fermionic systems, would benefit from a suitable semiclassical formalism that captures phase-coherent charge transport in real space. This talk reports on our recent work introducing "Orbital Wigner functions" as a suitable formalism. It combines Wigner quasi-probability distributions--a phase-space description of quantum mechanics--with coherent orbital dynamics. By testing the formalism against microscopic simulations, we illustrate its accuracy in capturing strongly non-equilibrium electron transport features not accessible by traditional approaches, such as the ballistic transport of a relative phase between microscopic orbitals. Our formalism offers a new approach to exploring real-space dynamics in systems where geometric and topological multiband effects are expected to be essential.