Pressure and Size Dependence of Roton Emission and Vortex Creation by Moving Objects in He II in T → 0 Limit: Generalized Nonlocal Gross-Pitaevskii Model

Abstract

In the framework of generalized, nonlocal Gross-Pitaevskii (GP) model, we study numerically the pressure- and size-dependent mechanisms of roton emission and vortex nucleation by objects moving in superfluid ⁴He. As far as the authors are aware, this is the first attempt to analyze the pressure dependence of these mechanisms and the associated critical velocities within a single theoretical framework. For each of several pressures in the range from 0 to the solidification pressure of ≈25 bar, we chose the parameters of the interatomic interaction potential such that the resulting excitation spectrum for the generalized, nonlocal GP equation approximates fairly accurately the pressure-dependent dispersion curve determined experimentally by Godfrin et al., Phys. Rev. B 103, 104516 (2021). In the two-dimensional approximation, for circular obstacles (disks) moving in quiescent ⁴He, we calculated two critical velocities — one corresponding to the roton emission and the other to the nucleation of quantized vortices — as functions of pressure and the obstacle’s size. We also comment briefly on three-dimensional simulations of the roton emission and vortex nucleation by moving spherical obstacles.