Phys. Rev. A, 2014, Volume 89, Issue 4, 41601, 5 pp.
Momentum relaxation of a mobile impurity in a one-dimensional quantum gas
E. Burovskia, V. Cheianova, O. Gamayunba, O. Lychkovskiycda
a Physics Department, Lancaster University, Lancaster LA1 4YB, United Kingdom
b Bogolyubov Institute for Theoretical Physics, 14-b Metrolohichna str., Kyiv 03680, Ukraine
c Institute for Theoretical and Experimental Physics, 25 B. Cheremushkinskaya str., Moscow 117218, Russia
d Russian Quantum Center, Novaya St. 100A, Skolkovo, Moscow Region 143025, Russia
We investigate the time evolution of the momentum of an impurity atom injected into a degenerate Tonks–Girardeau gas. We establish that given an initial momentum $p_0$
the impurity relaxes to a steady state with a nonvanishing momentum $p_\infty$.
The nature of the steady state is found to depend drastically on whether the masses of the impurity and the host are equal. This is due to multiple coherent scattering processes leading to a resonant interaction between the impurity and the host in the case of equal masses. The dependence of
$p_\infty$ on $p_0$ remains nontrivial even in the limit of vanishing interaction between the impurity and host particles. In this limit
$p_\infty(p_0)$ is found explicitly.
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