Mean-field construction for spectrum of one-dimensional Bose polaron

The full momentum dependence of spectrum of a point-like impurity immersed in a dilute one-dimensional Bose gas is calculated on the mean-field level. In particular we elaborate, to the finite-momentum Bose polaron, the path-integral approach whose semi-classical approximation leads to the conventional mean-field treatment of the problem while quantum corrections can be easily accounted by standard loop expansion techniques. The extracted low-energy parameters of impurity spectrum, namely, the binding energy and the effective mass of particle, are shown to be in qualitative agreement with the results of quantum Monte Carlo simulations. (C) 2019 Elsevier Inc. All rights reserved.