Kinetic theory for a mobile impurity in a degenerate TonksGirardeau gas
Abstract
A kinetic theory describing the motion of an impurity particle in a degenerate TonksGirardeau gas is presented. The theory is based on the onedimensional 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), 10.1103/PhysRevA.89.041601]. 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 steadystate 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.
 Publication:

Physical Review E
 Pub Date:
 September 2014
 DOI:
 10.1103/PhysRevE.90.032132
 arXiv:
 arXiv:1402.6362
 Bibcode:
 2014PhRvE..90c2132G
 Keywords:

 05.30.d;
 05.60.Gg;
 67.10.j;
 66.90.+r;
 Quantum statistical mechanics;
 Quantum transport;
 Quantum fluids: general properties;
 Other topics in nonelectronic transport properties of condensed matter;
 Condensed Matter  Quantum Gases;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Phys. Rev. E 90, 032132 (2014)