48 research outputs found
Reply to "Comment on 'Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas'"
In our recent paper [Phys. Rev. E 90, 032132 (2014)] we have studied the
dynamics of a mobile impurity particle weakly interacting with the
Tonks-Girardeau gas and pulled by a small external force, . Working in the
regime when the thermodynamic limit is taken prior to the small force limit, we
have found that the Bloch oscillations of the impurity velocity are absent in
the case of a light impurity. Further, we have argued that for a light impurity
the steady state drift velocity, , remains finite in the limit
. These results are in contradiction with earlier works by
Gangardt, Kamenev and Schecter [Phys. Rev. Lett. 102, 070402 (2009), Annals of
Physics 327, 639 (2012)]. One of us (OL) has conjectured [Phys. Rev. A 91,
040101 (2015)] that the central assumption of these works - the adiabaticity of
the dynamics - can break down in the thermodynamic limit. In the preceding
Comment [Phys. Rev. E 92, 016101 (2015)] Schecter, Gangardt and Kamenev have
argued against this conjecture and in support of the existence of Bloch
oscillations and linearity of . They have suggested that the ground
state of the impurity-fluid system is a quasi-bound state and that this is
sufficient to ensure adiabaticity in the thermodynamic limit. Their analytical
argument is based on a certain truncation of the Hilbert space of the system.
We argue that extending the results and intuition based on their truncated
model on the original many-body problem lacks justification
Momentum relaxation of a mobile impurity in a one-dimensional quantum gas
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 the impurity relaxes to a steady state with a
non-vanishing momentum The nature of the steady state is found to
depend drastically on whether the masses of the impurity and the host are equal
or not. 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 on remains non-trivial even in the
limit of vanishing interaction between the impurity and host particles. In this
limit is found explicitly