Current patterns in the phonon-maxon-roton excitations in 4He

The structure of one- and two-particle currents in liquid He-4 in the region of the phonon, maxon, and roton excitations is calculated using linear-response theory. A set of continuity equations is derived from the minimal-action principle. The two-particle current describes the motion of the He-4 atoms with respect to each other and thus enables us to identify topological structures. The optimized functional space makes no assumptions on the patterns and we show how a simple sound wave of the phonon excitation develops into an atomic-size backflow roll above the roton minimum at wave numbers k greater than or equal to 2.5 Angstrom(-1). The roll gets elongated in the direction of the center-of-mass motion and forms a tubelike structure of atomic diameter when k greater than or equal to 3.0 Angstrom(-1). The roton minimum itself is a resonance effect where the wavelength of the excitation matches with the wavelength of the oscillations caused by the two-particle correlations.