title: Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas.
abstract: A kinetic theory describing the motion of an impurity particle in a degenerate Tonks-Girardeau gas is presented. The theory is based on the one-dimensional Boltzmann equation. An iterative procedure for solving this equation is proposed, leading to the exact solution in a number of special cases and to an approximate solution with the explicitly specified precision in a general case. Previously we reported that the impurity reaches a nonthermal steady state, characterized by an impurity momentum p(∞) depending on its initial momentum p(0) [E. Burovski, V. Cheianov, O. Gamayun, and O. Lychkovskiy, Phys. Rev. A 89, 041601(R) (2014)]. In the present paper the detailed derivation of p(∞)(p(0)) is provided. We also study the motion of an impurity under the action of a constant force F. It is demonstrated that if the impurity is heavier than the host particles, m(i)>m(h), damped oscillations of the impurity momentum develop, while in the opposite case, m(i)<m(h), oscillations are absent. The steady-state momentum as a function of the applied force is determined. In the limit of weak force it is found to be force independent for a light impurity and proportional to √[F] for a heavy impurity.
authors.affiliation: Lancaster University, Physics Department, Lancaster LA1 4YB, United Kingdom and Bogolyubov Institute for Theoretical Physics, 14-b Metrolohichna Street, Kyiv 03680, Ukraine.
authors.forename: O
authors.initials: O
authors.lastname: Gamayun
authors.affiliation: Lancaster University, Physics Department, Lancaster LA1 4YB, United Kingdom and Russian Quantum Center, Novaya Street 100A, Skolkovo, Moscow Region 143025, Russia.
authors.forename: O
authors.initials: O
authors.lastname: Lychkovskiy
authors.affiliation: Lancaster University, Physics Department, Lancaster LA1 4YB, United Kingdom.
authors.forename: V
authors.initials: V
authors.lastname: Cheianov
mesh_terms: D005740:Gases; D007700:Kinetics; D009038:Motion; D011789:Quantum Theory
chemical_list: D005740:Gases