Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2014-09, Vol.90 (3), p.032132-032132, Article 032132
• Main Authors: Gamayun, O, Lychkovskiy, O, Cheianov, V
• Format: Article
• Language: English
• Subjects: Gases; Kinetics; Motion; Quantum Theory
• ISSN: 1539-3755; 1550-2376
• DOI: 10.1103/physreve.90.032132

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)