Classical and quantum dissipation of bright solitons in a bosonic superfluid

We consider the quantum dissipation of a bright soliton in a quasi-one-dimensional bosonic superfluid. The dissipation appears due to interaction of the soliton with Bogoliubov excitations, which act as a bath for the soliton. Using a collective coordinate approach and the Keldysh formalism, we derive a Langevin equation for the soliton motion which contains both a friction and a stochastic force. We argue that due to the integrability of the original problem, Ohmic friction is absent, rendering the dynamics non-Markovian. We furthermore show that the resulting friction can be interpreted as the backreaction of Bogoliubov quasiparticles emitted by an accelerating soliton, which represents an analogue of the Abraham-Lorentz force known in electrodynamic.