Motion of an Impurity Particle in a Boson Superfluid

Abstract

The problem of the low‐lying spectrum of a system of many bosons and one impurity particle interacting by repulsive, central, two‐body forces is treated by first eliminating the dynamical variables of the impurity in terms of an added effective boson‐boson interaction, and then treating the boson system by an extension of Bogolubov's method. In this way various physical properties of the clothed impurity particle, including its dispersion relation and effective mass, are obtained; singularities associated with the onset of acoustical wave drag as the impurity speed reaches the speed of sound in the boson medium are predicted. The parameters measuring the smallness of the corrections to the above results are shown to be the dimensionless boson‐boson interaction, the dimensionless boson‐impurity interaction, and the boson‐impurity mass ratio. The treatment is then adapted to the case of hard spheres at low density by employing the Huang‐Yang‐Lee pseudopotential method; the results are valid if the dimensionless boson density and the boson‐impurity mass ratio are small. A few remarks are made concerning the connection of the models treated with experimentally accessible results.