O. Gamayun

O. Lychkovskiy

Modelling the final state of a mobile impurity particle immersed in a one-dimensional quantum fluid after the abrupt application of a force.

A mobile impurity particle in a quantum fluid forms a polaron. For a fluid modeled by a one-dimensional gas of fermions, we calculate the distribution of momentum for such a polaron after a ‘kick’ that instantly delivers a finite impulse. A remarkable two-sided power-law singularity emerges in the distribution, which we analyse, deriving the asymptotic form of the distribution in the vicinity of the singularity.

A mobile impurity particle immersed in a quantum fluid forms a polaron - a quasiparticle consisting of the impurity and a local disturbance of the fluid around it. We ask what happens to a one-dimensional polaron after a kick, i.e. an abrupt application of a force that instantly delivers a finite impulse to the impurity. In the framework of an integrable model describing an impurity in a one-dimensional gas of fermions or hard-core bosons, we calculate the distribution of the polaron momentum established when the post-kick relaxation is over. A remarkable feature of this distribution is a two-sided power-law singularity that can correspond to one of two processes. In the first process, the whole impulse is transferred to the polaron, without creating phonon-like excitations of the fluid. In the second process, the impulse is shared between the polaron and the center-of-mass motion of the fluid, again without creating any fluid excitations. The latter process is, in fact, a Bragg reflection at the edge of the emergent Brillouin zone. We carefully analyze the conditions for each of the two cases and derive the asymptotic form of the distribution in the vicinity of the singularity.

A kicked polaron

One-dimensional Fermi polaron after a kick: two-sided singularity of the momentum distribution, Bragg reflection and other exact results