Mobility of Ions in a System of Interacting Bose Particles

Abstract

The transport property of an ion in a dilute Bose-Einstein gas subject to an external electric field is investigated by means of the Boltzmann equation. The interaction Hamiltonian which describes the ion-phonon scattering processes is obtained by the use of the Bogoliubov transformation and the cross section for the scattering of the ion by phonons is calculated. The solution of the Boltzmann equation is obtained by applying a variation principle and the temperature dependence of the ion mobility is shown to be $T^{-4\mathrm{}}$ at very low temperatures. A comparison of the results with the experimental data in liquid helium and the Khalatnikov and Zharkov theory is given and also the ion mobility in a Fermi system is briefly discussed.