Transport currents in Bose quantum liquids

Until now, most of what has been said about excitations in quantum liquids has concerned the dynamic structure function, which is observable by means of neutron scattering. The dynamic structure function can be calculated using standard linear response theory. However, at this level one needs only transition densities 〈0ρn〉 or transition currents 〈0jn〉, which are oscillatory in time and hence do not describe mass transport. In this work we go a step further and study transport currents in excited states, 〈njn〉, which requires the calculation of 〈njn〉 to second order. For that purpose, we take a well-tested microscopic theory of inhomogeneous quantum liquids and extend it to find the currents formed when helium atoms scatter off a helium slab or when excitations evaporate atoms (a setup experimented by A. F. G. Wyatt's group in Exeter). Current conservation was already a major theoretical problem encountered by R. Feynman and led him to introduce backflow corrections. We show that perfect current conservation is expected only for exact solutions of the time-dependent many-body Schrödinger equation. This is the first extensive theoretical study of transport phenomena in a quantum liquid based on an accurate microscopic theory.