Electronic transport and the hydrodynamic approach

Quantum dynamics of charge carriers remains one of the most important topics in modern condensed matter physics due to its common use as an important experimental tool and numerous practical applications. From the early days of Sommerfeld and Bloch to the recent discoveries of topological materials, free-electron theories have enjoyed a great success in describing observable transport properties of weakly interacting electronic systems. An extension to strongly coupled or strongly correlated systems presents a formidable challenge representing a major unsolved problem in modern physics. In a number of novel materials, the electronic system appears to be non-degenerate, making the applicability of theoretical approaches relying on the presence of the Fermi surface questionable. At the same time, the effects of potential disorder can be significantly suppressed by modern fabrication techniques. Recent experiments on ultra-clean systems at high enough temperatures show signatures of a collective motion of charge carriers similar to the hydrodynamic flow of a viscous fluid, the phenomenon with far reaching consequences in a wide range of many body systems from black holes to high-temperature superconductivity. At the same time, the connection between the nearly relativistic hydrodynamics in graphene and the holography approach to quantum field theory represents a promising avenue for theoretical developments.