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 p0 [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∞(p0) 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, mi>mh, damped oscillations of the impurity momentum develop, while in the opposite case, mi<mh, 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.
- 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
- E-Print:
- Phys. Rev. E 90, 032132 (2014)